Re: PSOne vs Saturn
Grandia PSOne was the weaker version.
Resident Evil Saturn was the weaker version (as posted above).
Doom and Hexen ran faster on the Saturn (although Quake II for the PSOne was better graphically than every FPS the Saturn had to offer-- but then there was no Saturn version to compare to). I remember Powerslave was quick on the Saturn-- but I never saw the PSOne version, though. Duke Nukem ran nice on the Saturn, too.
I doubt that games like Panzer Dragoon Zwei would port nicely on the PSOne. The game simply took advantage of whatever the Saturn has to offer (vast landscapes, mix of 3D and 2D elements). But since there's no PSOne version we can only contemplate.
DragonForce also makes use of the Saturn's features. It had lots of sprites to fill the screen. Although there is perspective, it's more 2D than 3D though.
Virtua Cop 1 was arcade perfect. I can't tell if Time Crisis was (never had it).
PSOne dominates the racing genre with Gran Turismo. Nothing can touch it graphically during its time. The best on the Saturn would be Sega Rally, albeit it had half the framerate of the arcade version and lower resolution.
Not all 2D games required the memory add-on. Even without it, games like X-Men, Darkstalkers and Marvel Superheroes looked better on the Saturn. For games that did require it, the Saturn leaves the PSOne versions to dust, offering more frames of animation, very fast loading times (KOF) and features (like the real-time character swap in X-Men vs Streetfighter).
I honestly felt that the Saturn version of VF2 was graphically better than the PSOne version of Tekken 2, with VF2's high screen resolution and texture resolution. But I must admit that Tekken 3 is much, much better graphically (even with slightly lower resolution). We never saw VF3 on the Saturn (it jumped on the Dreamcast, but there were rumors of an add-on card, but Sega axed that idea -- probably burned by the 32X).
Treasure's Guardian Heroes maxed out the 2D capabilities of the Saturn. But there were cases of framerate drops during some of the big boss fights. I can't remember anything memorable with the same genre on the PSOne (suggestions, anyone?)
Summary:
On purely 3D graphics, PSOne wins hands down. On mixed types (2D / 3D), it's a toss up (depends if the game used more 3D or 2D). On 2D games, the Saturn wins hands down.
It might look like a tie, but remember this was the mid 90's. People were switching from 2D 16-bit games to 3D 32-bit games. Whenever a 2D game was released, it was given a lower score for being "old gen". I remember the X-Men fighting game from Capcom got low scores on some magazines simply for being 2D. WTF??? I mean the game's almost the basis for the Capcom Vs games.
Sony also had a very good strategy (in a business sense) to prioritize 3D games over 2D ones, since 3D was the PSOne's major strength.
The PSOne also benefited from its built-in video decoder. FMVs looked better on the PSOne, while the Saturn either had to letterbox the FMVs or use the optional MPEG video card (only used by a few games). During this era, people put high value on FMVs (too much, I think). Imagine, developers were moving from the 32Megabit (4MB) cartridges to 600Megabyte CDs, so they really had to use those space. So the PSOne really had lots of 'wow' factor with it.
So there's my take on it.