I believe the Saturn can do texturing and lightshading in hardware.
Basically the only programmers who swore that the Saturn was a beautiful box of wonder that nobody was properly tapping were people working at or closely with Sega. Others, including the programmer of Saturn Quake (perhaps the single most polygon-heavy Saturn game) said that its architecture is stupid for 3D games, and that the Playstation is way faster at 3D drawing anyway.
The Saturn can do Garoud lighting using an additive model, but I'm not sure that works well with textured polys in most cases, thus many Saturn lighting examples are at least partially software in nature. I wish I understood what I just typed better than I actually do.
Saturn texturing is a weird beast. I get the feeling it does texturing in an odd way. I tried reading up on this, including the dev manual, so this is conjecture. The sprite and texturing engines are one and the same, and lots of different sources say that poly generation is somehow an extension of this engine, yet the Saturn seems to do 2D and 2D integration with 3D more smoothly and effectively than the Playstation. The Saturn architecture is a bit odd, and not nearly as straight-forward as the PS1 (which follows a much more traditional model, and also uses math shortcuts for speed, sacrificing accuracy), but I don't know that that means it is "stupid" for 3D games, despite what that programmer from Lobotomy claimed. He claimed the Saturn couldn't use one large poly for a wall, but instead had to use several small polys. This doesn't make a lot of sense without qualification. It is possible the Saturn can't do repeating textures on a surface, thus requiring multiple polys for a wall in order to get a repeating texture pattern, but even that doesn't completely make sense to me. It might have something to do with this information I found on the Rockin'-B web site: "The SEGA Saturn cannot change texture coordinates in game by hardware. This means that textures are pre-mapped and cannot change (except very few and very limited programming tricks, not worth mentioning) which is required for some of todays lightning effects." But I don't see how this would interfere with, say, making a big wall.
I want to know more about the Saturn, but it's really hard to find good info distilled into understandable terms.
I would say it was mostly hype.
JKM, yeah, in truth there's not much on the PS2 that the Dreamcast truly couldn't do. The PS2 can do some nicer visual effects and a few more polys in a scene, but PS2 texturing kinda sucks balls, and memory management on that console is a bitch. A quick and dirty port is, for the same effort, going to look less good than a Dreamcast game, and even the great games don't look too much better. Grand Theft Auto III had a large world but the textures were bland and the frame rate less than quick and smooth. The Dreamcast might have had trouble with the poly counts involved in far enough draw distance, but what you could see would likely look a lot better.