What we're dealing with here is finding the limits of human visual perception. One of the reasons 30FPS on a typical LCD seems "fine" is because the liquid crystals in the display require a finite time to reposition themselves in order to physically raster the requested image. This time is called latency, but the visible representation of that latency is actually a form of blurring; a cross-fade between each displayed image frame. In effect, an LCD will tend to slightly motion-blur the rapid sequence of frames, giving a sense of smoothness between the discrete images.
OLED, on the contrary, has astoundingly low latency; the organic light emmitting diodes activate near-instantly when charged, so in effect there is no human-perceptible blur between each frame. And just like looking at a desk fan, at lower speeds your eyes can make out the individual frames just like being able to discern the individual blades of a fan. At higher speeds, the frames finally start to blend together, just like the fan appears to become a smooth circular shape.
Why is there such a stark difference between 30 and 60 FPS? Because you're working to find the limits of a particular human's visual perception. The center of the human visual field is all about detail and not necessarily about visual change rate; peripheral vision is much more about fast motion and not so much detail. Beyond your organic eye's ability to perceive a faster refresh rate, a faster FPS game can still be perceived as even smoother. Ths is because input lag is tied to framerate, no small part of the "fluid" feel of a high framerate game is how connected the input feels.
edit: I left out a word at the very end! input lag is TIED to framerate...