The divine essence contained within each angel is finite and depletes over time if used. Originally angels didn't know this was the case as they were all within proximity of an infinite source of the essence and had no need to use their own stocks. Why learn to tap into your own reserves for a task that could simply be accomplished using the limitless emissions of the creator?

This all changed for the rebels after being cast out of heaven. Within the prison that they now resided in, they had to learn to sustain themselves solely off of their own limited stocks (and by cannibalizing the stocks of their fellow cellmates). For the first time, they learned what it meant to feel "hungry" and indeed later what it felt like to starve. The only upside of this new knowledge was that they became highly adept at controlling their inner flows of the essence and consequently highly adept at healing themselves after being injured.

Put simply non-rebellious angels control the divine essence that surrounds them while demons have learned to control the essence within themselves (they had no choice).

Of course, this "benefit" is really a small consolation compared to losing access to the source. After all, they are still constantly mal-nourished and thus weaker.

But why do they return to hell when "killed" on an alternate plane? Well, they don't actually return at all. They never left in the first place. The prison that is hell is just that: a prison. A prison that you don't ever fully break out of. There are "loopholes"/tricks to "escape" hell in a limited sense. But the core of their being can never leave it. One example of a loophole is possessing human beings. They're still very much in hell but they project part of themselves to remotely control a mortal. The small piece of the demon that you can exorcize from the human is like the demon stretching their arm through the bars of their cell frantically trying to sieze a piece of food (a tiny scrap of mortal essence). Now, if you really wanted to kill a demon for good you'd have to go down to hell itself... but that's not a good idea...

A demon will force their wounds to heal

Healing is, by definition a change from your current wounded state to a new "healed" state. But what does it mean to be "healed?" An angel or a demon may have a vision in their mind of what they want to look like and feel like when they are healed, but what about the stuff that they're made of? Does it have an idea of what healing is?

A demon will treat their body like clay, imposing their will on it. The demon will force the wound to close with sheer willpower, and force the cells to tie the wound shut (or whatever demons have instead of cells). This process is fast and powerful because the demon doesn't waste any time letting their body have a say. They know what needs to happen, and they compel their body to do it.

An angel, on the other hand, knows that life is sacred. Every little piece of their body has some will, even if that will is nothing more than some cells with DNA that tells the cell what to do. More importantly, each little piece has some knowledge or memory of what happened and what it is doing. An angel must first listen to their own body, understand what it wants to do, and then help guide it so that it heals themselves.

This process is much more difficult. It has to be done at the speed of the body doing the healing, rather than at the speed the individual's will would move. If anyone has done PT training after a major injury, you are aware of just how agonizingly slow this process is.

The result, however, is that the angel's healing is more "right." A demon may compel their wound to close, and the best their body can do is produce a bunch of scar tissue really quickly. Demon bodies may be covered in scars. Angels don't get scars. Or, if they do, it's because the angel and their body agreed that that was the best way to go. If you see an angel with a scar, it is a sign that you are looking at an angel who had to do the right thing in an enormously bad situation.

In the beginning, long before the events chronicled in Genesis, God created good and evil. Then, considering Himself to be good, and not wanting to be a hypocrite, he saturated all of his creations with fundamental goodness. Every part of the celestial substructure contains tolerances, biases and loopholes, such that no being living in that early creation could be harmed. This is the real purpose of the Angel's eternal incarnation. They live forever, and heal from any wound, so that God's creation (and by association, God Himself) cannot be blamed for their suffering and thereby be labelled evil.

So then, God's best mate, Luci, and the other angels, were hanging out in this first perfect matrix, when they realized there was a problem. Perfection is boring and boring is a form of suffering. Eternal beings, eternally bored and therefore eternally suffering, does not seem like a very good thing. They decided that God had better fix it quickly or risk being labelled the evilest being in all of creation.

They presented their problem to God, but He didn't understand what they were saying. God, being immortal on a totally different level than the angels, had existed for eternal time in total void and emptiness before He got the idea to start creating things. Boredom had become such a standard part of His existence that He no longer recognized it as suffering.

He did however recognize that the angels were calling Him evil, which was unacceptable. So he created "Oblivion". Any angel, in fact any aspect of the celestial creation, which found this boredom idea too intolerable to stand, had His permission to cease to exist. If however, a being chose Oblivion over boredom, that was their personal choice. God was not responsible and therefore definitively not evil.

Luci saw that God had missed the point, so he went back to Him and tried a different approach. "Hey Boss, do you mind if me and my buddies do a little creating of our own... something to pass the time."

God considered the request and, wanting to be a nice guy, agreed. But He also didn't want His beautiful creation messed up by the work of a bunch of angel amateurs. So he created "The Darkness", a terrestrial zone where the angels could play. He also wanted to give them a time limit for their diversion, so into the middle of the Darkness, He said, "Let there be Light" and a standard issue, 8-billion-year-lifespan sun came into being. "Luci, you have until that sun burns out, to play. Then I will look over what you and your mates have created and maybe promote your creation up to celestial level so you can play with it forever."

Happy with an escape from the boredom, the angels got to work on creation.

Four billion years into the game, God came to visit the garden which the angel's had created. He was impressed! The angels kept shape shifting into various animals to populate the garden, breeding to create genetically stable offspring of each of the animal life forms. Lucifer's snakes were especially beautiful in design simplicity. He was just about to approve the whole thing, when he noticed the human beings playing just outside the garden.

"What are they?" God asked.

"Not our finest work, Boss. We created them about fifty years ago... good body form, great posture and prehensile fingers... but we put a little too much grey matter upstairs. They are just a bit too intelligent to live in peace with the rest of creation. They stole an apple from that big tree over there, then they escaped the garden and set up shop for themselves over there."

"I don't like them." God judged. "You should exterminate them."

"We can't" Lucifer cried. "That would be evil."

Just then, one of the humans, a little brat named Kane killed his brother with a knife.

"Evil!" God Screamed. "Destroy them! Destroy the whole garden!"

And so the First Celestial War began with the angels defending their beloved creation while God and his loyalist strove to destroy it. God was severely hampered by His refusal to do evil, but being God, the angels didn't stand a chance. He won the war almost instantly.

Realizing that it would be evil to kill the angels, He created a prison and threw them in. To keep them from escaping their punishment by fleeing into Oblivion, He suspended that option for the incarcerated. Any prisoner who dies while condemned to Hell, immediately reincarnates in the deepest pit of Hell.

Meanwhile, the humans had gone forth and multiplied across the entirety of their planet. They were still mostly evil, but a few good ones were scattered about. God was very tempted to obliterate the entire terrestrial zone, but realize that the death of those good people would be blamed on Him. "Thank Me, that I put a time limit on that sun!" He sighed.

With that, He washed His hands of the whole project, content that it burn itself out over time.

Lucifer sat in the lake of fire, feeling his flesh crackle and his blood boil. He had to admit, it wasn't boring. Maybe the Old Man has finally learned something about entertaining His guests. We will have to keep working on His style, Luci thought, but He definitely has the intensity of living part right.

"Hey Boss!" Lucifer called. "You can't just leave them alone like that. Leaving the humans to their own devices would be evil!"

"You created them... so you take care of them!" came the Divine decree.

Thus the bridge between Hell and Earth was formed. Earth became the prison's outdoor courtyard; a place where the prisoners could get a little sunshine, exercise and blow off a little steam. The angels, went back to work polishing their creation with the hope that sometime before the sun burnt out, it would become acceptable to God.

The Great Age of Man began. The noble kingdom of Atlantis rose and spread prosperity and wisdom throughout the land.

Then one of the angels, Gabriel, asked God a question. "When are You going to let us out of this prison?"

God replied, "As soon as you destroy that evil world that you've created, or when the dying sun destroys it for you."

And So, the Second Celestial War began, not between God and the angels, but between those angels, who with Lucifer are trying to make their creation holy, and those behind Gabriel, who are trying to hasten Earth's demise and thus get out of Hell early.

This is where we find ourselves today, in a game of blood and dust between warring hosts of angels. Lucifer's forces clothed in light, leading those humans who would see us become acceptable for elevation to celestial status. Gabriel's forces clothed in soot and hellfire, leading humans who hunger for power over others.

Which is how we finally get around to answering Incognito's question...

• The demons reincarnate in Hell upon death because that is how Hell works. No prisoner may escape into Oblivion while assigned to Hell. The angels under Lucifer, who die also reincarnate in Hell, but since Gabriel's forces hold the lowest pits of Hell, any angel who reincarnates there, is chained and held captive, effectively out of the fight.



• 
  

  As for why demons regenerate faster than angels, that is a slightly darker tale...

  
  
  

  God's addition of a bridge to Hell was not a part of the Angels original plans for their creation. Its' presence skews several physical constants, allowing arcane energy to leak into our world. Those energies corrupt the natural balance, and among other detrimental effects, cause solar storms which hasten the death of the Sun.

  
  
  

  Very early in human history, power seeking humans learned how to harness these energies to horrific effect. The extinction of the Cromagnums, the sinking of Atlantis and countless other human tragedies were caused by human wizards seeking or wielding power.

  
  
  

  Over time, the demons have recruited these wizards to their side, trading power for power. The demons have shared Celestial knowledge in return for magical enhancement of their angelic form. It has cost them greatly in terms of aesthetics. "Handsome Devil" is now an oxymoron, but they have become stronger and now heal with supernatural speed.

  
  
  

  The angels cannot make similar deals with the wizards because every spell cast brings the sun's death closer. The release of arcane energies, which were never intended to be part of the terrestrial zone, fundamentally damages our reality. So the demons have had a major advantage and have been slowly winning the war for thousands of years.

  
  
  

  To combat this, the angels have fostered human learning, guiding us along the scientific climb. Only recently, we have learned the secrets of genetics which were part of the angelic design all along. We have finally gained enough knowledge to help the angels stand up to the magically bolstered demons.

  
  
  

  With genetic enhancement on their side, the angels are trying to turn the tables. They are still weaker and slower healing that the demons, but our genetics knowledge is rising fast. There is hope that very soon, our efforts will level the playing field.

  
  

In time and with great effort, we may be able to help the angels win; and then our world can return to the paradise-like garden, which it was always meant to be.

They're at a lower energy state.

Angels are beings of light. Demons are fallen angels, i.e, light that has been absorbed and retransmitted. It therefore takes less energy to recreate a demon than it does an angel, hence demons are more likely to respawn.

So that they cannot return to Heaven

They respawn because if they actually died, they might get sent to Purgatory and have a chance to 'earn' their way into Heaven. Similarly, they regenerate faster so that it is harder for them to die and thus find a way to game the system.

It is the nature of Hellfire

The flames of Hell of melted what god made. Made it soft, malleable. In a metaphysical sense, but also somewhat literally. As a result, the demons' bodies naturally meld and flow back into their original when damaged or deformed. And even when destroyed, the pieces are simply returned the crucible and reforged.

To punish them

@Willlik's answer, but in reverse. The more they stay alive, the more pain demons feel. It is their punishment from god, that their bodies can take more damage and their souls never find rest.

Mix and match

Pick one of the above for the reason for their regeneration and another for their respawn.

Your world's Yin and Yang are out of balance.

Much like the Greek Gods of old, both Heaven and Hell draw power from humans and their faith. However, they also draw power from humans' actions. Do-gooders and heroes give power to the Angels, while the Demons are fueled by the evil in the world. Unfortunately for your citizens, your story takes place in a Crapsack World (TV Tropes warning). Humans are constantly at war, crimes occur left and right, and your government(s) is/are utterly corrupt. In a dystopia such as this, your citizens are cynical and jaded, and very few of them believe in God or heaven, giving the demons even more power.

(Disclaimer: I hope this doesn't seems like I stole the answer, as it is related to John's comment on the question but this already was my first thought on this before seeing his comment)

It's just plain old evolution.
Angels live in a privileged, peaceful place, under God's grace and protection. Their lives are relatively easy and comfy and have not much to worry about, as most of their problems are treated by God itself.

But this is not the case in hell: this is a harsh place, a prison like you mentioned, where inhabitants constantly argue, fight, and hurt each other, and the law of the strongest prevail. The fallen angels, weakened by this place, are no longer immune to damage, they get hurt and scarred... but they're still immortal, and their bodies have to eventually heal or be healed.

With this new harsh cycle of getting hurt and healed going through many millenia, evolution does its thing: while their bodies cannot get harder as the material they're made of is already as hard as it can be, it surely can regenerate faster, as it got used to get hurt; not only that, but also their bodies begin to regenerate into new forms that would allow them to defend better and get hurt less while still hurting others more, hence the eventual growth of horns, fangs, claws, and all those things that make them very different-looking to the gorgeous angels they once were.

Demons are their own masters and heal by their own power.

Angels are servants of the creator and need everything they do, including healing, filled out in triplicate, run through the heavenly beaurocracy, approved, stamped, forgotten, re-filed, checked, signed, published for public commentary for three weeks and passed down formal channels to the implementation agency.

More or less, depending on how serious you want the answer to be. The idea being that Angels are part of a whole and things just go slower that way, and since their "bodies" are merely projections of their souls, healing being more or less optional is one of the things that gets shared ressources.

Suffering is part of God's plan.

Who can know the mind of God? Why does Creation include suffering? Yet it does, Angels like humans can feel pain and suffering and the angels experience of Creation is one way they worship the Creator, accepting the wisdom of the divine plan.

The demons are not into that. They have figured out ways to hack the plan.

Angels have to heal correctly. They need to be human shaped, without scars but with feathered wings. Healing to that shape is time consuming and requires concentration to direct the growth in the proper path. If they fail to follow this rule, they fall and become demons.

Demons don't have to follow the rules. The can heal into weird shapes with ugly scars. They can forgo wings or make them in weird shapes (e.g. bat-like). This is much easier and requires less concentration. So they could put more energy into what's necessary and less into maintaining cosmetic differences.

Demons also may have access to methods to make them heal faster that are barred to angels. For example, consuming compatible flesh and blood may be easier to convert into their own. But angels are barred from consuming human flesh or blood. Demons can not only consume humans but also plants, animals, and insects. What do they care if they start growing fur, scales, leaves, or an exoskeleton? They're demons! If angels do consume animal flesh or plants, they have to convert it into the right kind of flesh. Demons can just accept the consequences.