Aang would win because while Korra is all about brute force and ambitiousness, Aang is more agile and nimble. He can dodge Korra's attacks like a true Airbender, and eventually defeat her as Korra can lose her temper easily.
Korra could be a great fighter, but until she learned to move more nimbly, with not just force, then Aang. Cause, y'know, he mastered everything, whereas Korra still has a lot to learn. Course if she was as skilled as Aang, than Korra. Definitely Korra. heart
While Korra is a powerful bender to say the least, I think Aang would win. My reason for saying so? Korra doesn't have much self control. She is quick to attack and often does so without thinking things through. She is a very offensive bender who doesn't seem to focus very much on defense.
Aang, as stated by King Bumi is a master of avoiding and evading. Aang only fights directly when he has too and I believe that his defensive, evasive tactics would triumph over Korra's all out offense. Aang is shown to be able to keep a cool head under pressure where Korra doesn't seem to have that ability. So in a prolonged battle, Aang would have the advantage.
In my opinion, Korra is a fantastic bender, but I don't think she could win against Aang. That's just my opinion.
I think Aang...
Because even though he started off the same as Korra he still knew how to control himself a lot better. And self control is HUGE when fighting.
He knew his fears, weaknesses, and strengths.
Where as Korra hides her feelings and acts tough when she should let go....she's lost within herself.
She seems confused with everything about being the Avatar.
And unlike Korra, Aang learned what being the Avatar REALLY is about with years of experience.
Aang. Only because he has an easier time going into Avatar State. Korra uses a lot of fire and water bending when she fights but Aang is a natural with air bending and that would give him another advantage with his speed.