Well, I was somewhat interested by this. Yesterday, I pulled out my old PS1 (which hadn't been turned on in over 6 years) and connected it to my HDTV to play Chrono Cross. After turning it on, I was struck by one fact: it came in a hell of a lot better than my PS2.
The PS2 comes in extremely pixellated. The PS1 looked very smooth, though text was a little blurry. Actually, it looked almost like the PS3 upscaling + smoothing option for PS1 games (the PS3 represents text a little better). The PS2 is connected via component, while the PS1 was connected via composite. I'm guessing that's the difference, but I really don't know why that would be the case. The PS2 isn't outputting in progressive, so shouldn't it look the same as the PS1? Would it look the same if I plugged in composite cables? (I'd rather not try it until somebody gives me the affirmative.)
Anyone know anything about this? If my PS1 didn't have an obnoxious skipping issue (it's one of the older models with the melting parts), I'd probably hook it up permanently. I might even go to a flea market and pick up a PSOne.