The Nintendo 64 not only has full-perspective texturing, it can afford bilinear filtering — for each output pixel the PS1 samples the input texture exactly once. The N64 samples it four times and linearly interpolates according to how close it is to each (in two dimensions, hence bilinear).
The Saturn has a couple of tricks up its sleeve:
- the primitive is a rectangle, not a triangle; and
- it can do multilayer 2d backgrounds and Mode 7-type floor effects.
The Saturn gets to 3d by extending its sprite blitter so that they can be distorted into any quad. Which is a slightly tortured route, so the good Saturn games tend to have relatively simple geometry constructed from quads, and very low-resolution textures are common because you can't tile them without using multiple quads. So although the middles of each quad still shift around in a perspective-incorrect fashion it's usually less obvious due to the lower internal detail, and the lack of an obvious diagonal strut across each quad.
A disadvantage is that the machine has significant issues with clipping — check out any video of Duke Nukem 3d or Quake where the player walks along a corridor close to the wall. Quite a few PS1 games do a similar thing where rather than determining exactly where a polygon intersects z=1 it's cheaper just to push any vertices that should be behind z=1 forward a bit, but on the Saturn it's even more pervasive because even if you're lucky and a quad is trimmed so that it's still a quad, you can't adjust texture coordinates.
Sega themselves adopted a very low-contrast texturing scheme partly to hide that; if you watch something like Sega Rally then you can see the geometry distorting as it meets the camera, but since each quad on the floor is just different shades of brown, each hills is just different shades of green, etc, it's not obvious.
The Saturn also has an advantage for some kinds of game because of its support for Mode 7-style background layers, i.e. tile-based content that is distorted as the raster runs without ever being in a frame buffer, much like the Super Nintendo a generation before. As long as the camera doesn't roll, you can get perspective-correct drawing of floors and ceilings, correctly clipped. That's how Virtua Fighter 2 and all of the other fighting games that follow it do their arenas. So the backgrounds in those games are essentially free, and are never really rasterised in the framebuffer sense.