Certainly frame-rate and IQ matter. On PC, I have incredible difficulty playing things below 60fps. The experience is just flat out better.
That being said, my favorite game ever is a Zelda game that runs at 24fps all of the time. One of my favorite games last gen was Dark Souls, which on console (the only version that existed for years), dipped to 15 frames per second in multiple places. There are many great games that have dips. I can tolerate it on console. It won't "break" the experience for me.
It's not like the game runs at 20fps constantly. It has some stutters in crowded areas or with lots on screen every once in a while, and in this game it even sounds like we can correct those problems by going to mobile.