What a tough question. There have been a lot of great movie catfights over the years, and many of them have been mentioned here in this thread. One more movie I'll ad is Angles With Golden Guns. It's a mass girl fight, but I think it's the best mass girl fight I've ever seen. There are many good catball type fights. Here's the link to the fight:
https://www.youtube.com/watch?v=jBmHXow-RSgBut as for the best, if I was forced to name my favorite, I would have to agree with rin753....the fight in The Geisha is simply amazing. I think it is extremely realistic. The girls look like they are really slapping each other in the bathroom. The fight is extremely arousing, and as is pointed out, when they get into the other room, and they continue to fight although exhausted, when the one girl pins her rival on the table, and the one on bottom wraps her bare leg and thigh around the other girl, it's simply breathtaking.
Thanks for an amazing post.