The Saturn has hardware video decoding, but, when compared to the PSX, it all comes to what video format is natively supported.
The Saturn followed the 3DO way: Cinepak. It can be decoded it at no cost for the system.
The Saturn cinepak codec is very similar to the PC one. Try encoding a movie, 320x240 (or 320x224, the saturn res), at 300K/s, and see the quality... not pretty good, heh? Cinepak uses lossy-RLE frame compression, and the scene change detection is pretty poor crude.
The PSX used a MPEG-based video compression. It uses lossy-JPEG frame compression, and the scene change, while far from perfect, is more accurate than cinepak's.
Since JPEG compression is optimized for blurred images, and preserves smooth image areas, the PSX videos looks much smoother and anti-alised than the Saturn videos. The RLE compression, in lossy mode, bases itself in finding solid fill areas in the image, and compressing them. It has no native gradient detection suport, so gradient colors usually look bad in it. It can look acceptable if the videos uses lots of solid colors (ie: anime cutscenes).
Cinepak quality depends FAR more on the encoding than the decoding. If you ever tried making cinepak AVIs, you know that the encoding process is VERY SLOW, no matter how fast your computer is. The codec is veyr primitive and unoptimized.
Some Saturn developers managed to build their own, more optimized, encoders, as you can see some games, that clearly uses Cinepak, have much better video, that look smooth, and aren't that much blocky.
Check Radiant Silvergun, Lunar 2, Shining Force 3 (tought Scenario 2's intro is not very well encoded), and a few others.
Some developers (and Sega themselves) were unhappy with Cinepak, and experimented software-based codecs. There comes Duck's Truemotion.
It's frame and motion compression are far better than Cinepak's, being much less blocky, and it support smooth/blurrer images better.
The problem? Well, when running Cinepak, the Saturn runs at true color. But true color modes aren't freely accessible on the Saturn (they're kinda slow and are used only for cetain special corcunstances - cinepak is one of those), so the Truemotion videos used the defalut 16-bit color mode.
Since the the video colors look washed out when using only 65K colors, Duck implemented dithering (yeah, that same thing that PLAGUES most PSX games). So... truemotion looks like PSX games... dithered to death. But some games' videos did manged to look well enough, by using well balanced colors and contrast (Fighter's Megamix, Sonic Jam, Enemy Zero)
Also, a few games managed to use Truemotion at true color. I only recall DraculaX, but there are others.
And very very few games got thei OWN custom video codecs. Grandia is included.
Grandia's videos do look like they use MPEG-based compression. BUT, they run at high resolution modes, with 200% zoom (seems that was the only way Game Arts found to run them at truecolor), so the videos look pixelated AND suffer the hi-res tearing, a shame. Seems the PSX version .mov files are THE SAME as the Saturn version, but since they run at standard resolutions, they don't get teared.
Well, I also think Tengai Makyou IV uses custom codecs, since everyone says it's videos looks just as good as VCD. But I never found that game, neither to buy (considering my limits, of course) neither by ISO downloading, so I can't comment on it.