I can't really think of any other game that appeared on all three of these systems. There are games that appeared on the PS1 and Saturn, the N64 and the Saturn, and the PS1 and the N64, but this is the only game I can think of off the top of my head that had a port to all three. Doom doesn't count, because Doom 64 was a completely different game. All footage in this vid is taken on their original consoles running original copies of each game.
Anyway, this is a video comparison of Duke Nukem: Total Meltdown on the PS1, Duke Nukem 3D on the Sega Saturn, and Duke Nukem 64 on the N64. To be honest, I wasn't a PC gamer growing up, so I have only played small bits of the PC original Duke, so I'm not an expert on which is it the most true to the PC.
As for which version is the best, well, each has it's appeal. I really can't choose.
The N64 version has coop, and split screen multiplayer which is good, and it adds new areas to some of the levels (not to mention edited redesigned areas, but that's not a big deal), but the lack of music kind of drives me crazy.
The PS1 version zips by, but has some framerate issues. It also has a remixed soundtrack, but for some reason, the sound in the game is muffled. I could be my personal copy, but it doesn't come in to loudly on my TV for some reason. The PS1 version supports link cable multiplayer.
The Saturn version looks better and has a more stable frame rate than the PS1 version, but is slowest paced version. It's the one I'm most used to on account of the fact that I've had it for years, and only just recently acquired the PS1 and N64 versions. It's missing some things in the levels as well (it isn't censored like the N64 version though), but I still really enjoy the Saturn version. Plus it has a hidden game called Deathtank Zwei which plays like a four-player Worms. FPS games weren't in huge supply on the Saturn, so that still makes Duke on of the best on the system (Quake, Alien Trilogy, and Powerslave are also good choices). The Saturn version supported netlink for multiplayer.
I know fans of each version would like to weigh in on the matter, so what's your favorite console port of Duke 3D?
NOTE: This is not the best playing you'll ever see of this game. I skipped a few secrets along the way in order to make each playthrough as similar as possible.
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https://www.youtube.com/watch?v=OKOry-CGQ9c