They all have differences. The following was my analysis from a couple of years back:
OK, here's a list of the differences between the 3 versions that I noticed playing through all of them. Let me know if anything is incorrect, missing, or unclear. They are:
Super Famicom (SFC) version, developed by Quest PlayStation (PS) version, ported by Artdink Sega Saturn (SS) version, ported by Riverhillsoft
Visuals: The SFC and PS versions offer fullscreen visuals. The SS version introduces very odd resolutions with cutscenes displayed in a smaller box (like the compressed movies in other SS games) and with maps starting off with the sides cropped (sorta like yoko mode for shooters except not cut as much) and then, when you finally get control, are expanded to add more map to fit the sides without changing the resolution. Thus, all the sprites and portraits appear thinner.
Music: Each version has slightly different music, meaning both the ports have remixed songs. The PS version features simple symphonic tunes whereas the SS version has lower quality synth but often focuses on the harmony in the tunes, making some songs sound interestingly different from the other versions.
Sound effects: The SFC and SS versions use the same sound effects. The PS version is brand new and very crisp high quality.
Voice: The SS version exclusively has speech in most of the important cutscenes.
Battle saving: The SFC and SS versions offer temporary battle saves that disappear when loaded while the PS version allows permanent battle saving that remain when loaded. The SS version can get around the limitation of lost in-battle saves by using 3rd party memory carts to copy over the save data that contains the battle save.
Save capacity: The SFC version has battery backup with 2 permanent save slots available, 1 battle slot, and additional access to the Turbo File peripheral to store more saves. The PS version offers infinite save slots through the memory card with each save, whether a normal save or battle save, taking up a single block. The SS version offers 3 save slots and a battle slot on the system memory as well as additional saves through the use of a memory cart.
Loading times: The SFC version has no loading at all. Both ports have similar CD access times. However, the PS also takes the longest time to save a game whereas saving in the SFC and SS versions is instantaneous.
Stats: There are slightly different starting stats for Denim from the SFC version to the PS version. I haven't checked the SS version thoroughly.
Options: There are a couple of additional insignificant selections on the options screen for the ports.
Art gallery: This feature is exclusive to the SS version and is called the Deneb Report.
Glitches: The SS version contains an incredible glitch with the Ogre blade's BodyGrab ability that enables the player to obtain any unique leader. This means it's possible to have in your party all enemy leaders with unique portraits in Chapter 4 after Hell Gate can be accessed. Since this glitch isn't in the other versions, it almost seems intentionally added.
Thank you very much! Although the PS version is arguably superior, it appears that the BodyGrab glitch makes the SS version worth picking up too. With it one could create a dream-team that's impossible in the other versions.