PSX/Saturn
Both are basically the same game at heart so we'll lump them together.

Pros
>has music
>has the circuit tracks added along with the warrior PTO bonus car
>actually runs at something approaching a usable framerate and psx/saturn emulators are much more feature rich than 3DO emus
>has the bonus rally modes and the lunar rally track
>has the better looking time of day options

Cons
>No real analog support. The psx version supports the negcon but its kinda shit (tested on both emu and real hardware)
>time trial is more what you'd expect, just player vs stopwatch
>related to above that means to get traffic on you have to do a head-to-head race
>no x-man


Protip: at least in the psx version pressing down on the dpad for a few seconds hides the HUD - a feature that is in the rest of the EA made games.

PC
The special edition re-release has the most most content (only lacking lunar springs, though an unfinished version does exist in the code).

Pros
>actual analog support available both for steering and acceleration, but you have to fight dosbox as usual
>has time of day options
>has two unique tracks only found here
>has music
>best framerate out of the box

Cons
>time trial is more what you'd expect, just player vs stopwatch
>related to above that means to get traffic on you have to do a head-to-head race
>no x-man
>limited enhancement options due to being limited to the dos version. The windows version requires black magic to get working and isn't worth the hassle

OVERALL SUGGESTION:
Play the 3DO version but if that is a bit too raw play PC special edition.