It really worked somewhat like this...
PS1
Could do around 3500 textured polys per frame at 30fps at a resolution of 512x240. Unfortunately the polys the machine drew were almost the worst of any of the systems out there. The texture correction was the worst, seaming could be really bad, and polys would dissapear when turned on edge also you could not tile a texture across the surface of a polygon. What was good though was that alpha translucency worked extremely well. The 1 meg (or 1.5 I can't rememeber) of VRAM was quite good for the time.
Of course, when emulated on a PC now the games look better because everything was built with more polys and the poly drawing issues pretty much dissapear.
N64
Could do maybe 1800 textured polys at 30fps at 320x240. Certainly drew the most modern polys out there. Texture correction to stop warping, texture filtering to stop pixelization, z-buffer to allow cut throughs and long draw distances, mip mapping to stop texture moray at a distance, texture tiling, etc.
Cartridge actually made sense for the system spec but not its customers, developers, publishers, or its impression as a modern machine. Beyond that the low low fill rate and a lower V-RAM was the thorn in its side. Some game genres such as 1 on 1 fighting games just couldn't be done justice on it.
NHL 99 actually ran in a high res mode and a good framerate without the ram cart.
When emulated now you are only really gaining framerate and resolution to the image, nothing is really being added to make the title look more current.
Saturn
Could do maybe 2000 textured polys at 30 fps at 320x240. Drew the 2nd best polys. If I remember properly the machine drew quads instead of tris. Quads made the texture correction look a little better, seaming wasn't as much as issue, polys would not dissapear when turned on edge. Could not do translucency on a polygon basis, gourade shading took a extra bit of horsepower.
The savior of the machine were its VDP processors. This may be mixed up but the VDP1 would draw pant loads of 3D sprites and the VDP 2 could draw solid infinite planes (much like SNES mode 7) or backgrounds. Nights is a good example of the VDPs working overtime. The characters, their trail, and terrain are using the main geometry processor and all the enemies, rings, and other camera relative effects are using the VDP1. The VDP 2 was used for the far background, or in the case of boss battles, the floor. In sports games, the VDP 2 was used to draw the field so the polys could be put into the characters and stadiums.
The problem came from both its lack of upfront horsepower and the difficulty in getting all the chips to talk to one another.
In the end it all came down to the sort of games the developer wanted to make.
N64: Large scale environments.
PSX: Close combat or room based games, or racers with twisty tracks.
Saturn: Mixture of the 2 above but designed around a flat floor.
Had the N64 had more polypushing horsepower it would have steamrolled the two others. If the PSX just had a decent Z-buffer it would have produced some really incredible large scale games