Sozin's Comet arrives as scheduled, but there is a last minute change of plans. Ozai gives Azula the honor of burning the Earth Kingdom to ash in his stead. Aang goes to stop her instead of facing the Firelord in order to lessen the amount of damage caused by the Fire Nation while the Comet empowers them.
Round 1: Aang is EoS, but not in Avatar State(basically how he started the fight with Ozai). Azula is EoS and both are amped by Sozin's Comet. Azula's sanity will not be slipping in this scenario.
Round 2: Aang has access to the Avatar State, Azula has access to the Comet Amp once again.
Bonus Round: No Comet Amp or Avatar State, both are EoS.
Who wins? I personally have always wondered this since Aang really never got the chance to fight her again after the whole fiasco in Ba Sing Se.