I've been trying to spot the differences since one came out 3 years before the other one, but couldn't find the differences over the internet, even though some people hinted that some bugs and things were fixed on the ps version, like the fact that you couldn't be hurt as easily if you bumped against a wall.
It was also said that the pc version had better graphics/resolution

Please, any information would do ... to confirm these statements or add more...

What are really, the differences between those 2 versions ?

From what I can tell, the PS1 version has a quick save feature which the DOS version didn't have (and that helps immensely especially in the first dungeon of the game).

In the DOS version Twinsen can get damaged if he runs on a wall or any obstacle, not in the PS1 version thank God (it's super duper annoying I tell ya)

In the DOS version there's no on-screen UI, you cannot see your Health or Mana without calling up the menu

In the DOS version you can't select a different stance (Normal/Aggressive/etc.) without again, opening up the menu (there's a shortcut for each stance but it still pops up the menu for a second)

So in short, the PS1 version is an upgraded version of the DOS one