30 vs 60 vs 120 FPS

So I did a quick search didn’t find anything on this and was wondering. Do you think there are huge noticeable differences between 30, 60 and 120 fps? If so, by how much? Is 120 that much better than 60? Does the frame rate (not linked to logic) really effect game and by how much?

This is because some dude was ripping on me when I said that from 60 to 120 there isn’t such a huge noticeable difference. Most wouldn’t even care to notice.

Sorry if this was talked about already but I couldn’t find anything.