I used to not care at all about framerates until I played Dark Souls 2 on the PS3 at 30fps, I reached the Fume Knight and couldn't beat him after a few dozen attempts. Then a couple years later I played the PS4 version at 60fps, fought him again and managed to beat him without struggling nearly as much as I did with the PS3 version. It feels as if doubling the framerate from 30 to 60 also doubles your time to react, even though actions still happen in the same timespan.
For the most part I'll go for a higher framerate if possible, but if a game that I'm interested in only runs at 30fps or lower then I'll just play it that way and probably enjoy it just as much as any higher fps game.
