Hmm. I'm not disagreeing, but there's also the thing they were doing where Azula and Zuko are each other's shadows -- she's cool and efficient where he's hot-headed and ineffective, she is single-minded where he is conflicted, and so on. Which means that, at the end when Zuko overcame his various issues and became confident and focused, Azula had to become self-doubting and off-kilter.

This could perhaps be seen as an aspect of the show's critique of the Fire Nation philosophy -- or rather, Ogai's philosophy -- that life is a zero-sum game and in order for one person to win, another has to lose. This is in contrast to the whole-is-greater-than-the-sum-of-its-parts credo that the Gaang embodies. Zuko and Azula were trapped from their childhood in a situation where it was not possible for both of them to win at the same time.