The only time Azula got the better of Aang was when he was sleep-deprived and when she shot him in the back.
He beat her in a fair fight on top of the drill and she was running away from him the whole time during the invasion even after she got her powers back.
And to top it off she would have lost to her subpar brother in their final duel.
The only thing she has going for her is she's ruthless. Barring that she'd job to everyone.