Azula would have lost the Final Agni Kai no matter what. Here's why:
Azula is insecure. That's why she takes cheap shots. She did it with Katara, and she did it with Aang in CoD, AND she did it with Iroh striking him with lightning. One could even argue that her behavior in CoD foreshadows some of what happens in the Agni Kai, where in CoD, Katara fights Azula, and Zuko saves her, whereas in the Final Agni Kai, Zuko fights Azula and saves Katara. It's a little mismatch of dynamics.
Azula cheating (constantly), is a staple of dishonorable behavior, which I think is interesting.
We see her "play with her food" like a cat, with the Dai Lee and other opponents she encounters. She tricks them and manipulates them and there's no threat. Killing Aang with lightning was SUPREMELY stupid on her part, and she wouldn't have done it unless she was cornered. She didn't even stick around to make sure he was dead or have any of them followed-- because she was scared. Zuko NEVER flees in fights out of fear. He doubles down like a lunatic and tries to get himself killed instead. Azula is not willing to risk her life, and that's why she's a worse fighter. The insecurity gets to her head and she psychs herself out
Azula has a lot of fire power (lol), but Zuko has the heart and commitment to see actions through to the end. That's why he would have won, had Azula not cheated.
By the end, they were evenly matched in firepower anyway. They did the Raging Line of Flames Competing Colors thing and met in the middle, and stayed there. That's how animation tells us about their ability.
Azula's seat of power in her firebending is spite and fear. She's not even mad, bro.
Zuko's seat of power, at the end, is light and life and love. One is a powder keg that runs out after you blow it up once, and the other is like an oil fire in a parking lot. There's essentially infinite fuel there.
Zuko would have certainly outlasted her. And did, if you think about it. Because she panicked.
Azula's entire persona is a mask, just as Zuko's bravado and pettiness in the first season was a mask. (Funny, that he can only be himself when he's hidden the scar with the blue spirit mask, therefore freeing himself of the shame and the mark that brands him as a villain)
They show us that Azula's mask is not only slipping, but cracking, crumbling in the mirror scene. That's why it's there: to show the audience that all of her running has finally caught up with her.
This world that Azula created has been a sham from the beginning. Castles in the sky to make up for what she lacks: love.
Which is why she would never win against Zuko if they both reached their full potential, as they did during the comet.
