Based on what I know, other than the larger file size offerered by CD-ROMs, the PlayStation was outmatched by the N64 in most areas. Not by a vast degree, but it's what you'd expect from 1994 hardware vs. 1996 hardware.
PS1: 32 bit CPU at about 34 MHz, 2+ MB of RAM, 24 channels of audio
N64: 64 bit CPU at about 94 MHz, 4+ MB of RAM, 100 channels of audio
The PSOne's better looking games are more the result of developers and FMV's than the console being that powerful.
Oh, and textures. For some reason, the N64 had trouble with more complex textures.