I am often espousing the virtues of Grandia on the Saturn over the PS1 port, and folks often ask me why - I realize there‘s no real good explainer video with ALL the differences, which might be impossible, but I’m going to attempt to put most of the big stuff together right here.
The very first thing you'll notice is the frame rate in town is better on Saturn, and there are shadows to the buildings, which PS1 doesn't have. Also the sprite anchors are better on Saturn, whereas on the PS1 they kind of jerk around. Fair play to PS1, obviously there's better transparency, and they have sprite-based shadows instead of circles under characters. Also, critically (as @"◉◉maru"#146 pointed out) the ground textures are in the wrong place in the town - you can even see that in the video preview here, the house in the PS1 version is floating between two floor texture zones. You can see all that stuff in this video:
https://www.youtube.com/watch?v=UL6Z9xvt7h0
Some effects were simplified for the PS1 version, as you can see here:
https://youtu.be/XUkQoZGi3Uc?t=240
Then there's battles. To explain a bit, Grandia has a 3D world with sprite-based characters. But in battles, they use a bitmap for the background, because this lets them do 3D transparency over the 2D environment without issues, due to peculiarities of the Saturn hardware.
The PS1 has a nicer effect for getting into battle, but once there has a lower res texture for the battle map, and the zooms aren't as expressive, whereas the saturn texture is higher res and because of the odd jagginess of it better mimics the 3D environments you walk around in. Also the menus are transparent in the PS1 version but they're ugly on any version, I wouldn't say one's better than the other. I have a soft spot for dithered transparent 3D anyway, so my opinion is invalid here!
PS1: https://youtu.be/K2IvxpSKEWY?t=1037
SAT: https://youtu.be/MWMviQPo6V4?t=2095
PS1 magic effects are arguably nicer, it's down to preference
PS1: https://youtu.be/YUYEEJnUNwk?t=201
SAT: https://youtu.be/C-CkpyY361Y?t=592
personal pref again but I really prefer the look of the ghost fog in the saturn version. it fades in and out of intensity whereas the PS1 version is just a straight (very heavy-handed) transparent overlay:
SAT: https://youtu.be/j_LOFwcs_EE?t=12
PS1: https://youtu.be/FJfIoRohia0?t=3
These are all pretty subtle, but the biggest one for me is you'll get entire layers of sprites missing in cutscenes:
Saturn original: https://youtu.be/Jy3wRSWrxs4?t=1270
PS1: https://youtu.be/2rkdiatoEpY?t=761
Any of them are fine to play, but since there's an english patch out for the saturn version now, you might as well check that out!? (has instructions in summary)
https://www.youtube.com/watch?v=3g0gbnfNDZ8
AND you can also apply a widescreen hack and other screen effects to basically get yourself a saturn remaster in emulator!?
https://youtu.be/XUkQoZGi3Uc?t=150
There are more differences here and there of course. I mean heck, even the title screen is different.
https://youtu.be/df3iUDVF1dY?t=194
Again, not big stuff, but... it's sure noticeable! This is the the kind of thing I notice when playing through the game, and the reason I tell people to play the Saturn version, so... hopefully that helps somebody!!