| Who knows what will happen?
This answer is opinion-based, due to lack of canonical information to provide a definite answer.
Duel on Princess Azula's Ship → Victor: Azula when it was just the two of them, but Zuko eventually won that battle and was able to escape thanks to the intervention of Iroh.
- Zuko angrily charged her during this battle, but his lack of control made it relatively easy for Azula to gain the upper hand and in an attempt to demonstrate the extent of her skill, she began generating lightning. Before she could finish the form, she was interrupted by Iroh, who redirected the lightning and threw her over the side of the ship into the water.
Duel at Tu Zin → Victor: Azula was the better of Zuko, but Zuko, with the aid of Team Avatar managed in the end to make Azula run.
- After pursuing Team Avatar, Princess Azula finally came across her target, the young Avatar, Aang, in an abandoned town. Directly before the start of the duel, the exiled Prince Zuko joined in, hoping to regain his honor by capturing the Avatar and defeating his prodigious sister. Despite Zuko and Aang's best efforts, Azula was unstoppable. Zuko could only exchange several fire blasts with the princess before she was able to defeat him. Aang was soon trapped by Azula, but was saved with the timely intervention of Katara. Sokka and Toph soon arrived as well, along with Iroh. Azula, being outnumbered and cornered, surrenders. She quickly escaped however, by shooting Iroh with lightning while he was distracted. She protected herself from her attackers by creating a fire shield, and escaped the scene unharmed.
Duel on the Gondola → Victor: undecided
- Azula and Ty Lee attacked the gondola Zuko was using to escape from the Boiling Rock prison and as a result of this a big battle commenced atop of the roof of the gondola. While Ty Lee and Suki engaged in a fight, Sokka and Zuko faced Azula and held their own. When the Warden had ordered to cut the line, Azula and Ty Lee fled from to gondola, to prevent from falling down with it when the lines would be cut.
Duel on the Airship → Victor: undecided
- As Team Avatar escaped from Princess Azula's attack on the Western Air Temple, Zuko went to confront Azula himself. He found her on top of one of the airship's command towers. Upon asking his sister about the purpose of her attack, she exclaimed that it was a celebration of her soon becoming an only child, attacking Zuko after with a furious blast of blue fire, barely missing. He attempted to defeat her, but could only destroy her command tower before he fell into an abyss. Azula was sure of her victory, but was proven wrong when Zuko came back on top of another airship. The two fought furiously, though this time Azula did not gain the upper hand. The two then unleashed an extremely powerful blast of fire at the other, causing both of them to fall off the airship. Zuko was saved by Team Avatar, while Azula propelled herself to a cliff and used her headpiece to grapple onto the side.
Comet-enhanced Agni Kai → Victor: Katara (Zuko was winning initially, but was shot down by Azula when he caught a lightning bolt that was directed at Katara)
- Zuko and Azula started their battle by blasting enormous amounts of flames at each other. At first, the duel was relatively even, though Azula's further descent into madness slowly allowed Zuko to gain the upper hand. Azula then tried to kill Zuko by jetting around him and attacking him on all sides, but to no avail. Zuko got on the ground and created a fire tornado, knocking Azula to the ground and furthering her insanity even more. Zuko then taunted Azula for being scared to use lightning, as Zuko could redirect it. Azula took the bait and generated a powerful bolt of lightning. At the last second, however, she aimed at Katara, who was vulnerable. Zuko jumped in front of the lightning to save her. However, he could not redirect all of the lightning, which caused him to be badly injured. Azula then focused her attention on Katara.
Those were all the times Zuko and Azula faced off in battle against each other.