as far as I know, has the N64 a much more advanced 3d hardware(it supports perspective correct texture mapping, Z-Buffering and linear texture filtering, stuff that the PS1 lacks of, but really should be the minimum standard)
The problem though is that the N64 has less memory, static(in form of expensive cardridge ROM) and dynamic(main memory and texture memory). This is also the reason why most N64 games look rather blurry, because they have to use really tiny textures but they do have access to the more advanced linear texture filtering, which lets the textures be blurry instead of pixelated.