Katara hadn't entirly won yet in their fight in Crossroads, she had simply got a hold of an arm and leg.
At this point she could have indeed slammed her into a wall, but Azula is capable of firing with 1 arm or leg too, meaning there is a chance she could have broken free. This was also in a cave, meaning Azula had no access to the sun, making it the same as battling at night for her, yet Katara had a huge river that was right next to them at her disposal.
They seemed roughly equal in that fight, but you have to keep in mind that Azula would have been powered down due to lack of sunlight. Although I also got the impression that Azula underestimated Katara at first, seeing as how Aang could barely survive a battle with her, yet Katara just grabs her without to much trouble.
Azula has also shown the ability that if she doesn't want to get hit, she won't, seeing as how she was dodging all of Aang and Toph's moves during the invasion. This would seem to imply that Azula got a lot stronger in the last few months, seeing as how Aang could at least land a hit back on the Drill.
Course Katara has gotten a lot stronger too.
So the situation and location of the battle are the main factors here really. Course one lightning bolt is an instant kill here, seeing as how Katara isn't fast enough to dodge it and can't block it with water either.