The reason Quake probably looked better on your PC might've been because it was in a higher resolution, and was therefore less blurry, fuzzy and/or pixelized.
Because the PSP only goes to 480x272, it will look worse than it would at 640x480 (lowest resolution for modern games, though Quake can go as low as 320x200) or MUCH worse than it would on 1024x768. However, texture and model quality can't be adjusted no matter where you're playing Quake, so that's always the same. It's really just the resolution, which can't be fixed.
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