LoK or A:TLA?
 

Hm, that's a tough one.

Avatar the Last Airbender dominates in character development, on account of having 2 more seasons than LoK to develop them. The pacing in the first season is a little draggy, but beyond that it gets MUCH better, hitting that perfect line between a big grand story arc and easy to watch half hour segments. After you understand the concept, you can skip around a bit without losing too much, making it ideal for watching casually on Nick (if you did that in '06). The setting is perfectly constructed, with the characters living in this world so similar and yet so vastly different.

That being said, it IS a kids show, and it does show at times, with the simplistic humour and a tendency to end everything off with a moral of the story. There's nothing wrong with that, but it's something that gives Korra the edge.

The Legend of Korra is one of the few western cartoons that takes itself seriously. As in, it doesn't depend entirely on humour. In fact, it's main focus is the story arc (and the romance), which pays off for the most part (one could argue the ending was rushed, but come on! They had 12 episodes!) The colours are less bright, the style slightly less "cartoon-y". I prefer the setting in LoK. The combination of mystical powers with early 20th century technology creates a great contrast. It's even slightly steampunk in nature, especially the equipment of the Equalists.

Speaking of the villains, Amon beats Ozai any day. What a complex character! What great and actually relateble motivation! If Avatar the Last Airbender had one true flaw, it'd be the boring motivation of the grandest of grand villians.

As for the Avatars themselves, they're so different it's impossible to say who's more compelling. They both were told they were the Avatar younger than what is standard (to be fair, Korra figured it out herself). But the way they react is complete opposites.

Aang, at first anyways, doesn't even want to BE the Avatar. He doesn't believe he's able to take the responsibility. His spirtual side comes naturally, but he has problems with the idea of fighting, and will avoid it if he can.

Korra on the other hand, was THRILLED to be the Avatar. She LOVES the fighting, the honour brought by the role. Her spirtual side, however, is totally lacking.

They're so perfectly different you have to wonder if it was intentional.

In conclusion (TL;DR), both are awesome.