I love, love LOVE this topic. I could go on about Doom for hours. During my heyday I would switch between the 3DO, Jaguar, SNES, PSX, Saturn, N64 and 32X versions quite regularly (and also play some other games on those systems so as to not be switching them out fifty times per day). It took me a while to own a PC in those days, but my best friend did. He introduced me to Doom. One day I bought the SNES version and fired it up, and it was the best thing ever. Then I showed it to him. He immediately remarked on how terrible the graphics were. I made it my mission from that point on to find all the merits of the SNES version, while admitting all the faults, and I picked up more consoles (most of the time once they were no longer making games for them, thus these consoles were available for a very low price), and more Dooms. And they were ALL SO DIFFERENT! I loved it. It seems like every developer at the time went out of their way to make each Doom different from all the others, to give their console some way of competing, however trifling, and they succeeded.
The SNES version had great music. I noted that immediately. In time, I would discover that the 3DO had surpassed even the SNES in terms of musical quality, but in the meantime, the SNES music was amazing. The SNES levels were all identical to the PC version, albeit with horrible graphics in comparison. All the enemies were always facing you, gunshots were invisible, i.e. you couldn't see them if you shot the wall or something, and though it has no Spectres, the invisibility effect is superior to the original PC version. It's ultimately the same effect that the 3DO, Saturn and PSX have, but still...I can't recall what else the SNES had going for it at the moment, but hell, having all the levels intact meant the SNES offered a different level set than the other consoles, which made it a different experience.
The 32X version. Ah, yes, I remember firing that one up and being monumentally disappointed with the level selection. At the same time, however, I was mentally prepared to like the graphics more than I liked the SNES version simply because it was 32-bit as opposed to 16-bit (although supposedly the "Super-FX chip" inside the SNES Doom cartridge bumped it up somehow). They actually were a bit better, and I also remember thinking that the chopped up levels were actually modifications of the original levels--in other words, re-imagined versions which were meant to be superior. In retrospect, I dunno, I still think it was pretty cool that they were different, whatever the reason. I remember that the monsters could only face you on the 32X as well, and that it was missing invisibility/Spectres, the Spiderdemon and the Cyberdemon. It was pretty fast, I recall, had a pretty cool-sounding chainsaw and a very fast chaingun compared to the other consoles. Other than that? I'm not sure what it had going for it.
The Jaguar. Yeah, I have a feeling that's the one we've all been waiting for. A 64-bit console Doom. I thought, "surely this one is the greatest one yet" and "surely it will prove superior to the PC version". I didn't know a heck of a lot about computers and bits and graphics and whatnot at the time, so I was very excited to fire up an Atari Jaguar and play Doom on it. And you know what? I wasn't disappointed. Sure, the resolution wasn't up to PC standards, but the graphics overall were much better than the previous two. I remember noticing that there was no music in the levels, but really, after hearing the 32X music, I wondered if maybe there was a reason. I remember figuring out somehow that the items, monsters, weapons, etc. had more shades than the PC version or almost any other, due to seeing things in different light levels and in rooms where the lights were oscillating, for a more realistic effect. I loved the new levels, the tint of the rad suit and invulnerability were very cool and better than the PC. Oh, and I should note that one...interesting effect...was that on both the 32X and Jag I'm pretty sure I remember blowing up enemies with the rocket launcher from the opposite sides of walls. Not sure if I'd count that as anything but neutral. The lack of invisibility, Spectres, Spiderdemon and Cyberdemon on the Jag was sad, considering that it should have possessed the capability to show them, but at least the monsters could turn and fight each other. Ah! And the 32X and Jag both had a pretty cool blood effect when Demons bit you. Pixels of blood would splash up onto your face. Didn't look all that impressive, but it was still cool.
3DO. Sigh. It could have been so much better, but they made a valiant effort. I played it for a bit just because, and I have a feeling that an emulator for the PC would negate the sloth and choppiness that one encountered if one did not shrink the screen using the screen size option. In other words, the 3DO version was SLOW, but had a built-in fix which, well, sucked. The graphics were great and possibly close to being on-par with the Jag, maybe midway between the Jag and 32X. And it had invisibility and Spectres, but no Cyberdemon or Spiderdemon. The invis/Spectre effect was the same as SNES, superior to the PC. The levels were identical to the Jag. And the music. Was. Amazing. Seriously. Go to the Doom Depot website and listen to it.
Doom 64. Didn't play it as much as I should have, but it was so good! The lighting could have used some improvement and the levels were hard in an annoying kind of way--Doom is kind of about puzzles, but should never have been jacked up to that insane degree. I loved the updated graphics and think that Doom 64 is the quintessential example of what a 64-bit console can do. I also believe the background ambience/quasi-music was wonderful.
PSX/Saturn. I was impressed by the fact that these two updated both graphics and sound, with enhanced lighting perhaps close to or just about on-par with the Jag. I like that they had more levels than any other version, the same invis. and Spectre effect as 3D0 and SNES, Doom II enemies and weapons included in Doom I, the new levels and an excellent ambient soundtrack. I mean, seriously, between these two and Doom 64, I haven't heard anything like it. The Saturn falls short because it's choppy and slow at times, but I can't quite recall what its advantage was. I seem to recall it having at least one. At least! Eh. Oh! And all but the SNES gave 2% per armor bonus and health bonus instead of 1%, though there were always half as many of them lying around. But hey, it made more sense and was less annoying to run around and collect them all, huh?
I had the GBA version. Played it quite a bit at first, then misplaced my GBA! It's all I played on there, though. Great graphics for a handheld and really in general, although WHY was the blood GREEN? I suppose it's not a huge deal. It had all the same levels as the Jag and then Doom II as a follow-up...I can't remember any more!
So in closing...I can't pick a favorite. I like going back and playing the Jag and PSX versions and occasionally seeing stuff in Doom64, and if/when I find my GBA, I WILL PLAY IT! In the meantime, I'm working on getting a hold of Dooms I haven't played yet, and downloading emulators for a more rapid comparison/different Doom experience.
Any thoughts on my comprehensive run-down? Sorry for writing you all a novel here, just had some thoughts and wanted to share.