The ps-20 has 32 note polyphony when using the stereo sampled grand piano (that's the good one). The privia has only 16 note polyphony for it's stereo grand piano voice.
The px-300 has lots of sounds and accompaniment features which can be fun to play with, especially for kids, while the ps-20 only has a few sounds and no accompaniment features.
I really liked the touch on the pl-40r (same as ps-20 but with more features like the px-300) until the keys started clicking and I had to return it. The pl-40r was a closeout and as such had probably been shipped out and returned a bunch of times before I got it, so you probably shouldn't judge the quality of the ps-20 from my experience. In fact, I surveyed 5 ps-20 owners when I was deciding whether or not to try ordering another pl-40r again, and none of them reported any problems. If I could have found a brand-new-never-opened pl-40r I would have bought it.
The touch on the px-300 felt a little more "plasticky", not quite as realistic as the ps-20, but it wasn't bad.
You can find the manuals for both online at the casio web site.
I thought the touch on the p60 was comparable to the ps-20 and the piano sound was a bit better. The p60 has even fewer features than the ps-20: if all you want to do is play piano it's probably your best bet.
Your polyphony needs depend on what type of music you will be playing and how proficient you are. For a beginner the 16 note polyphony on the privia should be fine.
What will you be using the piano for?