I'm gonna have to go with the chaingun. It's a shame because it's really fun to use. But it has a very big shortcoming.
Compared to the shotgun, let alone the SSG or the more powerful stuff, the chaingun has an absolutely pitiful max ammo capacity, in terms of how much damage you can inflict with it -- see Fun Numbers below. It doesn't help that enemies drop very small amounts of ammo too, compared to the shotgun guy and his 4 shells. If the max bullet capacity was 400 (800 with backpack) it would've been a lot more useful. Basically, you can't do a lot with the chaingun before you're forced to go find more ammo. In my opinion this is the biggest flaw of Doom's weapon arsenal.
What's amazing is that Hacx makes this even worse -- its Uzi can be used maybe twice per level.
Shotgun -- 50 shells × 7 pellets each × ~10 damage each on average = ~3500 damage
Super shotgun -- 50 shells ÷ 2 shells per shot × 20 pellets each × ~10 = ~5000 damage
Chaingun/Pistol -- 200 bullets × ~10 = ~2000 damage
Rocket launcher -- 50 rockets × (~218) = ~10900 damage (~4500 w/o blast damage)
Plasma gun -- 300 cells × ~22,5 = ~6750 damage
BFG -- 7 shots [300 cells] × (~450 + 40 × ~68) = 3150 [balls] + 19040 [tracers] = ~22190 damage