The most common problem i see when people talk about frame rates is almost no one talks about input response times. You can have 60+ fps and have a sh*tty experience if the controls feel laggy because of some additional issue or bug in a game, or for example if the frame rate is high but unstable. Sadly this sometimes can happen. On consoles games are normally conceived to be played at the frame rate the console can achieve and this is the the biggest point they have in their favor. People tend to turn it into a number contest but things are not always that simple. That's why some games feel terrible at 30 or even 50 fps while in consoles they might have lower fps and still feel more responsive.
All that said, if there's no input lag at all, having more fps is always, objectively better, preferably synced to the monitor refresh rate to avoid tearing or dropped frames. Anyone who refuses to admit that is either misinformed or just kidding himself. And don't even get me started on "cinematic feels", "human eye can only see n frames per second", and similar delusions.
(How's that for a rant? )