Input lag, character movements and animations. Frame rate does affect the controls, in fact even in the xbox version of bayonetta , there were moments of framerate drop and they were annoying. Best example of controls is DMC, framerate was stable, less input lag, smooth animations and movements.
Edit: bayonetta on ps3 ran at +30, still annoying and affects the overall quality of the game and high level play. You can react better, have better control, have precise inputs during certain frames and have smoother animations on high frame rate. 60 is ideal, below that really hurts the gameplay , especially for fast paced action games and fighting games with precise inputs.