PSVR2 demonstrates the difference between 60 and 120 all the time. All the 60 fps reprojected games have a completely different feel and look between stick turning (60 fps) and head turning (120 fps). There is no smooth analog turning at 60fps, hence snap turn or increasing the stick turn rate to treat it like mouse look. (or turn very slowly) Very different from sitting on a merry go round at high speed and get natural motion blur (before throwing up lol)
But it depends on screen size, with VR obviously having the largest possible screen. Or rather it depends on the distance that things 'skip' between frames.
You eyes pick up multiple frame above 30 fps. The human eye's frame rate is flexible, depends on light input and other variables, sits anywhere between 30 and 60 fps. Your eyes also track moving objects to keep the same area of your retina focused on a moving object to collect 'data' of what you're looking at.
At 60 fps, if you turn circles with the analog stick (constant angular turn rate) you see multiple frame overlapping. Natural motion blur doesn't work since your eyes get exposed to discreet frames that get blended together on your retina. Same when following a moving object across the screen like a mouse pointer. The more frames, the smaller steps it make, the easier it is to follow and look at. The bigger the steps the more it jumps across you retina and you see more than a single mouse pointer. Just move the mouse pointer back and forth over a black background, at 144 hz I can see about 8-10 discreet pointers if I move the mouse up and down quickly. If I change my display to 60fps I only see 5-6 pointers with the same movement. So double images (seeing multiple frame together) already starts over 12 fps. The human eye has high persistence.
The only perfect frame rate there is is when the fastest moving object doesn't skip a single pixel while moving over the screen. Of course there is also an upper limit of being able to track objects. You can follow a baseball with your eyes, not a bullet.
The maximum speed for smooth pursuit in adults is around 100°/s, which translates to roughly 17.5 mph for an object 5 meters away.
100 degrees is about the fov of VR headsets. So at 2000x2040 per eye, you need 2,000 frames per second to be able to follow objects without any judder.
At 20/20 vision, 60 pixels per degree, over 100 degrees that's 6,000 pixels per second you can track. 6,000 frames per second to eliminate any judder. That's the upper limit, but at the same time we can perceive motion at 12 fps. That was the going rate for animated movies and stop motion.
Of course the only thing that does is turn seeing multiple mouse pointers into seeing a streak/smear. Hence motion blur works to make things appear to move more smoothly. However motion blur should work together with eye movement so smooth pursuit still works. Eye tracked dynamic motion blur is a better solution than brute forcing frame rate.
For gaming, the better you can track / follow targets with your eyes the better you can aim at them. Hence higher fps is better for competitive gaming. The reaction time difference is negligible if input lag is already well below human reaction time (200ms). Movement looks more clear / sharper at higher fps.