Subjectively for me, the biggest difference comparing the 20fps, is between the 15fps, rather than the 30fps.
This isn't subjective. The differences you'll see the between the 15 FPS and 30 FPS range are much more apparent than the differences between 30 and 60. Anything beyond 30 is varying degrees of smoothness, from good to great.
From my experiences, higher framerates have a more noticeable impact when it comes to moving about in an environment than it does for character animations. For instance, if you were to compare two similar looking characters side by side, one done with 24 frames of animation, and the other 48, you would notice smaller details on the character with the higher framerate, like he might do something with his hands between frame 5 and 10 than the lower framerate character doesn't do, but both would still move realistically. That's because the eye (or the brain) applies a good bit of interpolation when it comes to animation. It has a tendency to fill in the blanks. You don't need a perfect gradient of frames between positions to achieve realistic looking animation.
But the eye (or the brain) doesn't do as good of a job at filling in the blanks when it comes to large scale movement. Like if you were to compare someone pivoting around at varying speeds in an FPS game at 24 and 48 frames per second, you'd see a marked difference between the two.
And like I said earlier, when you're in direct control of what an image does, you tend to notice missing frames a little more. Like if you're tracking a character in your little onscreen targeting reticle, you're more aware of the gradient of frames between, say, moving your point of view between a tree and a bush 10 feet away.
This is why high framerates in games are more important than they are in movies. It isn't the animation exactly, but the fluidity of movement while looking around and moving through an environment. We expect it to look more like what we see with our own eyes, which of course doesn't interpret the world in frames, but in arcminutes.
edit: oh, and the difference between 60hz and 120hz LCD TVs isn't about fluidity of motion...well, sorta, not exactly. It's about being able to display fast moving objects better. This is kinda hard to explain, but...well...you'll only ever mentally account for 60 frames per second regardless. But if something like a bird or a ball were to pass really quickly from left to right on the screen, the 120hz TV would be able to maintain the image of it without making it look as blurry or juttery.
If you watch a ton of football and baseball, you'll want a 120hz screen. But if you spend most of your time watching movies, you'll be good either/or (unless you're watching a Bruckheimer flick).