The PS1 was custom designed to run 3D games. The Saturn was not. It had a second Hitachi CPU added late in its design in a vain attempt to match the announced specs of the PS1, resulting in an unbalanced design. It couldn't handle transparencies, and the number of polygons it could render was far lower then the PS1. Saturn 3D games usually ran in a lower resolution (Saturn had a couple of high res modes which it used for 2D gaming). The Saturn was a 2D powerhouse, but the world had moved into 3D and polygons. As Sega knew well, as they were pioneering this in the arcades, yet failed to bring this tech into the home.
Bolded false statement.
At a developer standpoint, it's true PSX it's better designed. Easier to develop, cheaper to manufacture, good performer overall. The best Sony machine so far along with Vita.
But Saturn was more powerful. Playstation had a bunch of fixed hardware functions to handle graphical effects such as aforementioned transparencies or video playback. Saturn didn't. That doesn't mean Saturn was unable to handle them, just developers had to code them by software. The good old fixed hardware vs raw power battle.
Saturn have more Ram to store textures and do not have that PSX Trademark horrid low precision texture deformation, have better hi res modes, etc... So you can't say Saturn wasn't ready for 3D rendering.
Thing is, ask back then at 1995 to code for dual main CPU's without a proper SDK, when even today there is a buch of monothread code out there. SEGA's results were growing exponentially, every generation of games put in shame the former. There is nothing close to leaked Shenmue footage on PSX, but that wasn't the rule.
PSX it's a better console hardware since it is close to full potential in most of the games. Cheap hardware, cheap tricks to render, okay, but it looks better with less investment.
And, of course, it's wrong that Saturn was designed to 2D. Hitachi developed SH2 as a cost efficient all around performer. When Sony used SGI based R3000A, they just can't deliver the same performance on a single chip, that's why they went the 2 chips way. They didn't have the tech.
And, of course, those are not Saturn VF3 screenshots. Just look at the resolution or aspect ratio. Just old glitchy model 3 emulation.
Sorry for the derail. There is a lot to talk about Saturn, but this is not the thread.