Yeah, I actually started my X-COM career on the PSX version. It had better smoke, cutscenes, neat loading screens, turned black backgrounds into this weird purple cloudy image, better sounds...
And it made the controls in the DOS version look beautifully intuitive. Imagine using a D-pad to move the mouse pointer around the screen. X is left click, O is right (you could open doors without walking in on PSX). The other option was a hot spot interface, in which each tile and button on screen was a "spot" you could select with the D-pad. This was a little better, until you realize they never coded in a way to open doors in the hot spot interface.
You also only had one save per memory card, and the loading times were atrocious. This was especially bad because the game always chose to get stuck either on a loading screen or on an alien activity screen; this didn't stop the slow pulsating animation "Loading..." and" ALIEN ACTIVITY" had, though, so you were often left wondering if it was stuck or just trying to calculate every alien's movement in a super-packed alien base.
The cutscenes were pretty great, though. I wish there were a way to swap out the PSX ones with the DOS narratives and intro, but hey. They were cheesy early 2000's CGI, anyway, so I guess it's not so important.