This is essentially the same as the age old Goku vs Superman argument. It's really gonna come down to what each fan boy/girl prefers since most people just say that their favorite thing is superior.
Each of the fighters in this contest would have advantages and disadvantages. Depending on who's fighting whom you'd have very different results. If say you had Aang vs some random student from the college of Winterhold Aang would destroy them. However, if you had some extremely powerful mage like a Psijic or Arch-Mage vs someone like Bolin then it'd be a massacre as well. This whole thing is just highly situational.
For the sake of the argument I'm going to use three people that I would consider to be relatively equal in terms of their power:
1) The Avatar Korra who is capable of using fire, water and earth control but has yet to master air. She has the Avatar state which is extremely powerful, but she cannot really control when it happens.
2) The Arch-Mage of the Arcane University who defeated Mannimarco. The Arch-Mage of Oblivion defeated an evil cult that had the power of the King of Worms on it's side and could raise an army of the dead. He almost certainly would have known every school of magic and been highly adept at using them in combat. However, he would have the disadvantage of needing mana to use his abilities, and while as the Arch-Mage he probably has a sizable mana pool it could still run out in a long fight leaving him defenseless (I'm assuming that he would have been a pure mage and not a battle mage for the sake of this argument because if I took into account everyone's characters that finished that questline I'd have to make him a Mary Sue and a half).
3) "The Full Metal Alchemist" Edward Elric. He has the power to use alchemy without the need of a transmutation circle and has proven his abilities in battle against the Homunculus and many other enemies. He can create weapons out of everyday objects and even the ground he walks on, and is damn near unstoppable when enraged. His weakness would come from not being able to use his powers without equivalent exchange, so if their wasn't something around that was worth the object he needed he'd be s.o.l.. Ed is also extremely hotheaded and doesn't seem to think things through before doing them which could be a problem in a fight with ranged attackers like his opponents in this fight.
I see things being fairly even at first with the Arch-Mage causing massive damage after emerging from an invisibility spell and unleashing the fury of arcane fire, lightning and frost. Ed would have no problem avoiding serious damage by creating shields out of the earth through alchemy. Korra could avoid much of this as well with her earth bending. Korra's attacks would be easily repelled at first by the Arch-Mage's wards, and Ed's agility would keep him on his toes and out of danger. Ed's attacks wouldn't be as effective in the beginning because they're almost all physical and close range so he'd be playing D for a good while.
I see the Arch-Mage tiring faster then the others due to age (yes we don't know his actual age, but it's fair to say that he's older than both Korra and Ed who are in their late teens or early 20s). If he doesn't get lucky and make a hit early on then the Arch-Mage is the first to go in the fight. His mana would run out and without it he'd be blasted to Oblivion by Korra or cut down by Ed. After the Arch-Mage's attacks are out of the way I see Ed being able to focus more on dodging Korra's attacks and closing the gap to attack. Korra, however, is no slouch and wouldn't be an easy target. Korra also seems to have a sense of humor and almost certainly would piss Ed off with insults.
Ed being a hothead would fall for the name calling and begin to attack in a fury without really thinking causing him to be open for multiple attacks from Korra. Korra's pride I think would play a role though and I see her getting in close to meet her attacker head on for the final blow. This mistake would be her downfall, however, as when she went in to meet the unarmed Elric she'd be met with his automail being transmuted into a blade.
As Ed moves in for the kill though a bloodied and beaten Korra is saved as the Avatar state engages. In shock Ed tries to run, but the unstoppable monster that Korra has become destroys the entire area and Ed along with it.
Winner: The Avatar Korra!
In the end I see Korra's Avatar state being the deciding factor here. -If- she was somehow ended early on by say the Arch-Mage's fireballs or something (which is a possibility seeing as she isn't a flawless fighter and one hit from the Arch-Mage could be enough to cause an instant kill) then the Avatar state wouldn't have time to engage and the fight would go in a completely different direction. I think the fight would, however, come down to either Korra or Ed winning. The Arch-Mage is powerful and probably the heaviest hitter of the three, but mana dependency and lack of physical skill means that he's a master of only one trade. Unless his initial surprise attack with invisibility worked or he got a lucky hit he'd be quickly worn out by the younger and more fit combatants.
Ed and Korra both suffer from being hotheaded and headstrong, and both would likely taunt each other during the fight. However, I see Ed being effected by this more and letting himself slip up. Korra would not win though without the Avatar state as I just don't think she has it in her to end someone. At least not without being forced to or doing so when in the Avatar state's rage. Ed I don't think would have as much a problem with this, though it wouldn't be a cakewalk for him either.
Anyway it's like I said, this is all situational. If Korra hits the Avatar state she wins, but if she doesn't then it's probably Ed's game. The Arch-Mage is going to factor in, but unless he gets lucky early on I just don't see him (or any pure mage from the Elder Scrolls) winning this fight.
Didn't know Korra could use air now as I haven't seen it in a while. Need to get back to watching lol. Regardless I don't think that it's going to have a major impact on the fight considering the Arch-Mage can use multiple elements too, and air bending wouldn't really be worth much in a fight outside of being used to keep enemies back similar to the unrelenting force shout.
I say Ed would be a top contender in this fight because 1) He's young and in top physical condition (He's shown to be very muscular and can accomplish things that most average people couldn't), 2) He's far superior in close range combat to either the Arch-Mage or Korra and 3) Korra, despite her Avatariness isn't anywhere near as powerful as Aang or the other Avatars of old.
I used Ed also because of his ability to transmute without the need of a transmutation circle which is a HUGE bonus. Other alchemists would need to stop everything to draw this out before unleashing a powerful attack. Now I know some people have overcome this with certain things (i.e. Mustang's gloves, etc.) but Ed doesn't need anything at all. He's also the main character of the series and accomplishes A LOT by the end of the series that most people wouldn't have been able to. Another reason I used Ed is that he's the best all around candidate from FMA. Others have abilities that would have come in handy, but they also all focus on just specific skills whereas Ed is a jack of all trades. This quality I think makes Ed the best choice to fight the Arch-Mage (also a jack of all trades) and Korra (the Avatar who can use all the elements).
The Arch-Mage I think would fare far better if he had access to mana potions in this fight. It would almost certainly change the outcome if he could replenish his mana pool mid fight. However, I refrained from giving them to him because I just felt that that would make him slightly OP. I'm also going by the assumption that this fight wouldn't be something the combatants would be prepared for, and despite our giant sized pockets in the games I don't think that lugging around 50 potions at all times would be very easy in a more realistic setting.
These are all perfectly plausible scenarios, however, they're all situational as I stated before in my post. We're assuming here that it would be a blood bender vs the others and in my opinion that just makes things far to unbalanced. It's like putting the Arch-Mage against some kid who just learned to bend really.
Using Scar, Isaac or Kimbley is also a bit OP. Like a blood bender they have abilities that only they can use and that are damn near unstoppable. However, they could be beaten IF Korra or the Mage knew that their abilities required them to be in close proximity to use. This again requires something that is situational though (i.e. the knowledge of their opponent before the fight begins).
I picked the people I did because I wanted this to be as fair a fight as possible with none of the combatants knowing that the fight was going to happen or what their opponents' skill sets were.
True but Elder Scrolls gods have been beaten by regular mortals too. Goku was already probably powerful enough to beat and Elder Scrolls god during the original series so him become a god himself is like... well I don't really have a comparison here. Sufficed to say he'd probably eat Akatosh for lunch and leave the entire realm of Atherias in ruin before heading to Oblivion to wipe out all the Daedric Princes with one spirit bomb.