As a result of a video I saw recently on pcper, there was a claim that high refresh rate monitors (100+) do offer a visible difference over "only" 60fps. They suggested it can be one of those things where once you have experienced it, you can't go back. Well, I actually bought a monitor to try that out. Just a budget 144Hz 1080p panel. I loaded the original Portal so as not to be too demanding and able to easily achieve high framerates. Yup, you can see and feel the difference. It wasn't massive, but it was there. Note this was almost a side by side comparison. If you were to try one, then at a totally different time the other, it might not be so obvious. Since I'm not a twitch gamer, this level of speed doesn't matter to me so I'll stick to 60Hz monitors (although I am tempted to go G-sync next time). I'd also add, TN monitors aren't as bad as I remember them being. Maybe I can be less of an IPS snob.
Separately to that, can >60 fps on a 60Hz monitor feel better? Yes, as it can reduce latency between when the frame (or part thereof) was drawn and actually hitting the screen. Nvidia even put a new feature into the 10xx series cards to do this with vsync on. In cases where the GPU can do more than a couple frames per refresh, it will do so and display the last one thus reducing the latency between what's shown and what's happening. With traditional vsync it just draws a frame then waits around to show it, adding latency between what you do and see.
