As micampe said, you're mixing refresh rates with frame rates, but actually you aren't entirely wrong, because I remember the heady days of upgrading my graphics card and having Counter-Strike hit 100-120 frames per second on my 120 Hz CRT monitor, and the visual difference was very noticeable vs. when I was back in 60fps zone.

The main visual difference was when rapidly moving the mouse; turning quickly was much more visually appealing at a high frame rate.