Those two weren't cutting edge back in 1996!
See SCUD Race from Sega (an arcade Model 3 game).
Yes, the screenshot is from an emulator, but I assure you that contrarily to N64 screenshots this arcade board rendered very clean graphics, even when transparencies were involved.
The only thing that makes most N64 games bearable these days are emulators, they fix the frame rate drops, they fix the low quality texture filtering, and bump the resolution, sometimes you even have texture packs to make the game look like something, this machine did not have enough RAM to do what it wanted to do properly.
At least the PS1 had the space to accommodate a decent amount of 2D backgrounds, so you could overlay those early 3D models on them (not good for all games, but certainly practical for many others), the PS1 could also push more raw polygons, had more RAM left to store textures (ie. the textures were bigger than what the N64 could handle, but the machine did not filter them).
So the PS1's drawbacks against the N64 were these:
- No texture filtering (given the quality of the filtering on the N64 I would say it's a plus)
- No perspective correction on textures (warped image - cured by emulation)
- No, or limited Z buffer
- No analog stick on the first version of the controller
- only two controller ports
- No RAM upgrade like the N64 and Saturn had
- Very limited storage offered by cartridges
- Very expensive storage
- It could handle less raw polygons per second
- Texture filtering looked very dirty
- Small texture cache prevented games from using detailed textures, they had to be blurry
Look at Ocarina of Time without filtering:
That game would have benefited from more memory in all places, but back in 1996 that wasn't necessarily a choice if you wanted to sell your consoles at a decent price.
Also, be careful when some people put pictures of games that used the expansion pack, it added RAM and resolved a lot of problems.
Look at what they managed to do when porting Quake II on the PS1
And an image with texture filtering
Way more detailed and better lit than its N64 equivalents as far as I know.