First, let me say that I love both shows because they never talk down to their audience, they have good ideas.
AtLA: This series is just a classic. Every small detail about it was so, so right. It seems like every character had development, points of interest, motives, drives. Almost every character had their own quirks, and full, well-developed personalities. The series really was great start to finish, and even the odd filler episode was worth watching.
And season three was just a flat-out masterpiece. The character development was just a joy to watch, and the finales were a joy to watch. The fights were well choreographed and the first between Zuko and Azula struck juuuust the right note of tragic. The way they handled Azula's clear mental illness still gives me chills, in a good way.
LoK: This series was rushed, but I understand why. Each season had to be a complete story because no one knew if it would be the last. First they thought season 1 would be the only season, then when season 1 was a hit, they were contracted for season 2 and so on.
So it was rushed, but I am willing to overlook it for the sake of fairness.
LoK has a much, much more refined art style than Avatar, and I do really love it. It's not quite what avatar was stylistically, but it is definitely great. The backgrounds are breathtaking, the characters look great, and the fight choreography, MY GOD THE FIGHT CHOREOGRAPHY IS JUST GORGEOUS. I WANT TO MARRY ALL OF THE ANIMATORS INVOLVED. ALL OF THEM.
Season 1 was really great. I enjoyed the bender v nonbender conflict, and I wish they would've had time to do more with it. My BIGGEST gripe is the deus ex at the end of the season where all of Amon's damage was magically undone and there were no lasting consequences.
Season 2 was a trainwreck. They started off being interesting, I liked the political themes of unrest between the northern and southern water tribes, and I wished they'd done more with it. I almost gave up on the series because of this season, though...
And then Season 3 renewed my faith. Every episode was interesting, the villians were insanely awesome. The fights were awesome to watch and it was a ******** SOLID season from start to finish.
In short: between the two, I think AtLA is better as a compete series. The emotional highs and lows were much better than anything LoK has brought to the table. There are so many things in AtLA that still make me blubber like a big baby.
LoK is cinematically superior. There's really just no arguing that in my mind.
And I think the best season in the series is a tie between both LoK season 3 and AtLA season 3.