IMO, It's kind of a mixed bag. I've played both PC and PSX versions of AE and AO (even though the PSX versions were in German, but they're essentially the same game anyway just with different voices).
The PC versions of AO and AE run a lot faster than the PSX versions (but your decision making has to be quicker because of this), and loading times are quicker too, but sometimes the sprites and sounds lack quality due to the conversion process from PSX to PC (in AO, it's barely noticeable, but it's quite noticeable in AE).
However, PC screens normally have a lot higher resolution than most TVs, so all the graphics are crystal clear compared to the PSX version unless you have a HD TV or so. Equally you're more likely to have a better sound system connected to your PC rather than your TV, so you're probably better off with the PC version to get the full Oddworld experience.
In the end though, the PSX versions are the original versions, and play how they've been designed to play. The PC versions do glitch majorly sometimes, and like other people have said here, the controls are different - You need to be used to a keyboard to enjoy playing the PC versions, unless of course you have a game controller attached to your PC.