The difference is noticeable to me.
Any good gamer will be able to tell the difference right away as it influences things like reaction times/responsiveness. In fighters every move has a number of frames for example. Every frame can make the difference.
Every game benefits from it from a visual standpoint as every animation will be twice as smooth.
For a casual gamer that doesnt even try to execute well, yeah maybe they don't even bother to try and notice it. But i can tell that whoever says that 60fps doesnt matter, doesnt put much effort on their gaming. Because its a huge thing. If you honestly don't see the difference i can only conclude its a physical problem.