Generally speaking I find specifically for shooters, the higher the frame rate the better, consistency also helps a lot. The more frames you can see it feels as though the target is moving slower, its easier in your mind to track things, to know how far ahead you have to put your cursor before you hit the mouse click. Fluctuating frame rates can really mess with your mouse aiming as you set your sensitivity against a specific frame rate, losing those frames will cause it to jump. Also, sometimes things move just the slightest bit at a distance, or your limited time to react to something is so small that without having high fps, you couldn't have seen it, or be given the advantage of reacting to it. Overall, I think for competitive play, I'll always go with higher frame rate over all quality of the graphics. If 60fps is the highest it goes, for competitive play I'd always want to see 60fps.
I can see why MS has been so adamant on making H5 60fps, as they are hoping this is going to be their eSport game. Hopefully it pays off for them