I shoot with both my index and middle fingers. As mentioned above, I started out with my index finger and shot thousands of rounds that way. One day I tried using my middle finger and found I shot more accurately. I shoot 9mm and 40 S&W CZ's so my index finger is not in the way of the slide or the escaping gases although my finger has a lot of residue on it when I finish shooting. I wouldn't use my middle finger on most other designs.
All that said, I recently got disgusted with my shooting and went back to using my index finger. In the end, I don't think it makes much difference one way or another for me.