I'm bumping this because I've had the same questions.
I've read reports that some movies are added or missing, and some of the missions are missing or have been replaced with all new missions. Some sources claim its not that different, while others claim its vastly different.
Oddly, all the reports I've read state that Wing Commander III
is improved on the Playstation for having more story sequences (including one intended for the PC but not included for some reason, something about a traitor), while the PSone version of Wing Commander IV
is reportedly inferior.
It seems like at this point all you can do is play both games and see for yourself.
It has been a while since I first posted this question. Since then I have played the Playstation and PC versions of both games, so I can report on the major differences.
Wing Commander III:
The video sequences in Wing Commander III look better on the Playstation version (less pixelated) and there are more videos. There is a series of TCN News videos that are not included in the PC version. Also there is a scene where Hobbe's leaves a message for Blair explaining his actions which is not in the PC version. In flight the graphics look very similar to the PC version, but there is no cockpit art. There is only one control scheme, but I personally don't find it too hard to use. The main problem with the controls is that this game came out before the dual analog controller, so you have to use the D pad for steering. As far as I can tell, the game includes all of the missions from the PC version except that the ground based parts of the few missions that included a ground component are replaced with cutscenes. You just do the in space part and then once you reach the planet it goes to a cutscene.
Wing Commander IV:
The video sequence in the Playstation version look ok, but are more compressed than those from the Wing Commander III port apparently due to the inclusion of stereo sound instead of mono. The DVD edition of the game has the best looking video sequences by far. The Playstation version loses a significant amount of video sequences that add more to the characters but are not really necessary to follow the story. The Tyr missions were ground based in the PC version but were replaced with space based missions in the Playstation version and were given new wireframes in the briefings. The Circe missions were completely removed. Instead of giving you a choice to go to Speradon of Circe, the game just takes you to Speradon without giving you the choice. The in flight graphics look like a lower resolution version of the PC graphics. The PC version's HUD looks a little different and the ship explosions are more realistic. The Playstation versions gives you multiple controls schemes and supports the dual analog controller.
About the ESRB rating:
From what I can tell, the primary reason, if not the only reason, that the PC version of Wing Commander IV got an M rating and the Playstation version got a T rating, is because in the original PC version the scene where Seether kills Paulsen is apparently very bloody. I have never watched the scene but I know what happens in it. The scene in the Playstation version lets you know what happened but shows no blood or gore. The DVD version of the game has both versions on the disc for some reason but plays the Playstation version of the scene. The DVD version was not sold separately in stores but was included in a PC DVD player pack, so the company may have just not bothered to get the DVD version rated separately.