Doom had multiplayer (although back in the day it was difficult or expensive to line up an actual game unless you were lucky enough to have a home lan).
On the other hand Dark Forces was a deeper game (and harder too). You could jump, aim (up and down anyway), crouch, and all the weapons had secondary fire modes. Plus there were some 3-D objects.
DF and Doom both had extensive mod communities and tons of free mods to download.
On the other hand in the modern day, Doom & Doom2 have the source ports and other things and now full internet play (Doomconnector for example) free.
Dark Forces on the other hand really hasn't improved any since that time. There are still a lot of mods, but the addons for Doom can make the game have almost modern graphics.
It really would be cool if LucasArts would either release the source for DF or else a patch for 3D acceleration, higher res, etc. like they did for a few of their other games (X-Wing, TIE Fighter, XvT, Outlaws). And maybe even a multiplayer patch (rumor has it that multiplayer was worked on for the game, though no idea how far along it was or if the code even still exists).
Overall both are fun games to play, but with DF you're stuck with the primitive graphics, there's no way to improve them (though the Mac version I'm told is a bit easier on the jaded modern eyes).