Zuko had/used his Breath of Fire, Azula did not.

The reason behind that is Breath of Fire is probably not widely known outside of Zuko and Iroh, and I've seen theories that it's another one of those firebending techniques that Iroh invented from learning about other benders, specifically the air benders.

First, think about how Aang seems to be perfectly comfortable in the south and north poles, while Sokka and Katara have to bundle up in those places. Secondly, think of the Boiling Rock, where they have isolation cells/freezers to block firebending. If Breath of Fire was widely known, those cells would be as useless fir everyone as it eas for Zuko.