I definitely agree about stepping up the rewards on higher difficulties of certain special levels, and with most of what Game Hunter posted. As to specifics...
-Hell's Arena on N! *is* a platinum badge, and ought to be incredibly difficult. On a standard game, I won't even enter it without a combat shotty, and I'd rather have some kind of powerup and chaingun to boot. (Chain gun is pretty much guaranteed on N! by the time this level generates... even on UV.) That being said, I think a plasma rifle should spawn instead of the chaingun. Not sure about a medpack or two, but both would give incentive to move around instead of just spamming shotgun shells from behind a pillar.
Awards:
AoB: A random weapon of the melee variety, heheheh. Seeing as how it's the most difficult challenge mode to defeat the Arena on, it seems only fitting the award be good as well. Chainsaw, butcher's cleaver, or perhaps DS can be generated! (Hehehe, imagine the rage at getting the chainsaw generated or maybe even a combat knife o_O. Okay, maybe rule out the combat knife and just stick with a Cleaver.)
AoMr: A blaster would be a heavensend, although perhaps a bit OP? Granted this challenge is next to impossible, but I would fall in love with the idea of a random exo/uni pistol. One of the main challenges of a pistol game is feeding that ammo consumption rate, after all. Since the normal Arena rewards and the AoB rewards both serve to help gain access to the Wall, perhaps an Anti-Freak Jackal (which ought to be an exotic imo) could be awarded?
AoSg: An easier Hell's Arena challenge, I would also like the idea of a random unique/exo shotty. Double shotty at this stage is a decent reward, but maybe drop a power mod as well on N! ? Even though these are difficult levels, I'm sure dropping uni/exo gear at such a low level would cause balance issues. That said, would certainly be nice, if perhaps a bit OP.
AoPu: I love the idea for tailored rewards for these challenges, would give actual non-exp incentive to enter. Definitely ought to replace the supercharge globe with some med kits, since AoSg and AoMr tailor their awards for their specific challenges respectively.
AoLT: Curious why you'd replace the cells with boots, it's a strong assumption that boots are better suited to AoLT game. Backpack would be nice on N! of course, but you can already get it at the wall. One of the main reasons I always try to clear Arena no matter the difficulty is so I can get enough rockets to comfortably blaze through The Wall and go for that backpack and Missile launcher.
-The Wall has the best rewards out of all the special levels imo, given the stage at when you come across it. The backpack is a great space saver and the missile launcher is one of my most favorite weapons in the game. Just as useful on N!, don't see why that would need changing.
-Hell's Armory should *absolutely* have a guaranteed exotic/unique on the other side. It doesn't even guarantee that it fits a current build, but compared to the other nearby special levels the rewards are kind of week, although the mods are nice. It also doesn't make a lot of sense, here are all these soldiers carrying around plasma rifles and chainguns, and they are guarding a storage of 4 shotgun/pistol etc. >.<
-Halls of Carnage has more health than is really needed imo, although a bit more difficult on N!. A bruiser brother at the end wouldn't really make story sense, but wouldn't be a bad buff to the level. Although if you aren't corner shooting, the current enemies are already formidable.
-Hellgate. Heh. On N!, fun stuff. A supercharge globe would be fantastic, but the two large healing globes encourages you to run away to hide in the little room from Hell, giving you that choice of turning back or pressing forward after the first wave of monsters come. Good stuff as is. (Yes, Hellgate on N! is a nightmare, but aptly so.)
-Vaults I absolutely agree. Having Vaults with no exotic or unique items generated is just silly. Clearing them is enough of a pain and requires a solid marine that having one or two random uniques or exotics won't make a game breaking difference that deep in Hell. It seems like the Vault awards have gotten toned down recently, after entry into the vaults becomes more and more public knowledge.
-Clearing special levels on N!. After a special level has been cleared, it should stay cleared, this seems fair enough. "Bringing Peace back to this evil place" followed by being assaulted by Barons of Hell doesn't seem to make much sense.
-Lava Pits. I agree that there should be a good chance of spawning at least one piece from the Gothic/Phase set, seeing as how they are almost impossible to compete in any given game. So having one piece of gothic or phase set would increase incentive to tackle this difficult and otherwise unrewarding level.
One issue with a lot of these suggestions is that it only serves to make N! easier, when the direction we are headed in is making N! harder. I agree that some rewards need to be scaled, but it's going to be tricky to scale appropriately without overdoing it.