Why don't I have a custom title by now?!
This is due in no small part to the fact that Doom's source code was unusually highly portable -for a video game of its era, and well beyond it-, so it was relatively easy to port the game to other platforms while leaving most of the mechanics and gameplay intact, and even a good deal of the game data. Also, none of the platforms it was ported to required severe resolution or color depth compromises to the point of having to use different resources (actually, they all were capable of indexed 8-bit color, plus all had the capability of playing back multichannel digitized sound, and the ability to use about 4 MB of addressable memory space between RAM and ROM, if need be).
Overall though, Doom seemed to get slightly better treatment when being ported than some games from that era did.. So many AWFUL versions of Street Fighter 2 out there during this era, holy crap.
The only ports clearly diverging in look and/or feel, as you said, are the SNES and the GBA Doom 2 port, and in general any port which is based on a different engine or is a complete rewrite.
Compare that with the situation of games that started off on arcade machines, home computers or home consoles: each further port of the original was basically a more or less complete rewrite from the ground up, usually having only unportable assembly (!) code or just mechanics observation for reference, not a highly portable engine written in a high-level language and already neatly modularized. And let's not even speak about the graphics and sound: those almost always need to be retouched or redrawn by hand, in order to fit a different palette, lower color depth, lower resolution, inability to play back samples, smaller memory etc.