@arcus: Because of how they were portrayed (example: Toph causing an earthquake that even Kuvira was surprised about, sayingnher daughters were bad metalbenders, Katara being basically the greatest healer in the world, etc.). When she told Korra her reasoning for not helping against Kuvira and Katara not helping against Unalaq, I think was the writers telling us: "Yeah, they'd probably wreck these guys, but this is about Korra." They are the new Jeong Jeong and Pakku and Bumi to me. I would say the same if this thread was "Aang (water bending only) vs. Jeong Jeong." And Azula, I would have already considered to be one of the greatest firebenders in the world from a very young age (younger than Korra).
As far as feats go, Azula's got just as much raw power as Korra, and more agility, smarts and cunning. If it was a simple, straightforward fight, I think the faster one would take it, so Azula. If it was a fight that had tricks and resources involved, the smarter, so Azula again. One element isn't enough.
She has a wealth of metal at her disposal since the fight takes place in Zaofu, and Zuko can't bend lightning. Against a metal/earthbender, I'd say that was your best shot. He can also be dumb in combat from what I remember (not trying to hate, I actually believe they purposefully write him to be this way), while I think Lin was one of the most resourceful members of Team Korra.
@arcus: Uhhh, Azula had Aang running while she was multitasking between him and Zuko. As soon as you're recovering from her fire, she's on the move. I'm not saying it's a trump card, but I do think that Korra won't be able to beat her restricted to waterbending. Katara is a more formidable opponent for Azula IMO because she is resourceful and creative, rather than headstrong and obvious.