N64 was miles better at the time. Today PS1 holds up better.
PS1 had terrible graphics even for it's time.
A lot of PS1 developers made overly complicated textures that wound up looking like pixel soup on the PS1's horribly small texture files. Just imagine taking a photo of a brick wall, turning it into a texture, and then saving it as a JPEG a hundred times. The grainy pixelated result is about as good as what a PS1 game texture looked like. You couldn't even make out the features on Snakes face in MGS. He had no nose, eyes, mouth or anything. It was a godawful mess.
N64 did the smart thing and filtered textures. The result was a more cartoony look for most games, but a look that holds up better by today's standards. They also had the expansion pack to make textures look better.
PS1 had virtually no anti-aliasing. Edges constantly bounced around everywhere. Screenshots do not do it justice. Combined with the awful textures, most PS1 games look like pixel soup.
PS1 didn't have any groundbreaking games at all. The best PS1 games are RPGs, 2D platformers, and 2D fighters.
N64 moved the industry forward with Goldeneye, Perfect Dark, Ocarina of Time, SM64, Analog control, Four player split screen, and rumble.
Most PS1 games never even took advantage of the analog sticks on the Dualshock. Sure, you could use the analog sticks, but they'd just give you the same input as the D-Pad.
In the end the PS1 wins though, because all the JRPGs hold up very well. Goldeneye and Perfect Dark both aged horribly. Ocarina of Time, Starfox 64, and Majora's Mask are now on the 3DS. Super Mario 64 has aged badly along with other platformers of it's time.
