Aang wins. Especially if they have Avatar State access. He was much more in touch with his past lives and even at only 12 years old his iceberg feat surpassed pretty much anything Korra has done. All of his AS feats are so much higher and better than hers.
I figure she'd win because every Avatar is supposed to be more powerful than the last and have all of their knowledge/skill. Like even if she hasn't showed the raw power and feats it should be acknowledged that it's there because of the Avatar cycle I'm not the most knowledgeable on Avatar so I may be wrong though.
Every successive Avatar isn't more powerful than the one before them. They just have access to their wisdom and foresight to help them should they need it.
Also, being in touch with the spirit world and connecting to them helps, but the true strength from the Avatar State comes from mastering the Avatar State itself and your spirituality as Guru Pathik pointed out. But even before he mastered it, Aang's demonstrations with the Avatar State blow Korra's out of the water.
Potentially, but it doesn't seem so. It's more for wisdom when it comes to combat or situations, not making you better in a fight.
The one time I can think of channeling a past Avatar actually gave you their skills was when Aang connected with Kyoshi and she actually took on her physical form using his body as a soul anchor and used her powers.
If Korra had access to Aang's skills, she'd be a whole lot more effective when she used the Avatar State.
People seem to be ignoring that fact. You can compare the two feat for feat, episode for episode, Avatar State to Avatar State and Aang is vastly more impressive.
Also more impressive is the fact that Aang is 12 years old, and has had far less tutelage in Earth, Fire, and Waterbending, yet has still been called a Master by other Masters and still shows better feats than Korra despite her training in all the styles except Air and supposedly mastering them since she was a toddler. Aang didn't even use another element until after he'd escaped his iceberg.
Korra is more spiritually sound? Aang was a monk. Spiritualism and Meditation was who he was. Also he went in and out of the spirit world on a whim, regularly talked with Spirits, even had casual and in depth conversations with past Avatars.
Korra couldn't even get in without help from Jinora. On top of that, it was pointed out many times that Korra's biggest weakness was her reliance on the physical nature of bending and not the spiritual element. Also her temper which kept her from attaining control over her spirit and the spirit world.