Modern Vintage Gamer recently posted a video describing why the PS1’s graphics sometimes “wobbled”, while games from the N64 wouldn’t exhibit the same behavior.
In short, the answer is a combination of the graphics chips, as well as the buffering and scaling capabilities of each. On original hardware, this would often result in the PlayStation having a sharper look that exhibits these issues, while the N64’s graphics are softer, but mask the problems. Interestingly enough, PS1 emulation can “fix” this on PS1 games and you can remove the wobble.
As always, I recommend watching the video for a full explanation, filled with awesome examples, but here’s a quick example: