The above makes me think of a different topic: Weapons I never found viable.
Shotguns. In Fallout 3, the Combat Shotgun was the premier close-quarters firearm. At any given stage, shotguns have low DPS, low range, and extremely poor performance against armored enemies, though Slugs or the Shotgun Surgeon trait can help that. They just don’t have any advantages, any at all. In theory they might have a large alpha strike, since they tend to have a relatively high total DAM provided all 7 projectiles hit, but in practice they never have enough for a one-shot kill so it comes down to DPS again. Maybe they’re useful at Normal difficulty, where they might one-shot things?
Grenade launchers. Low DPS, and since they fire in an arc, the shell almost never lands where you think it will. I suppose they could be useful against long-distance targets behind cover, provided anyone actually stayed behind cover long enough to use one.
Incinerators. Same problem as the grenade launchers.
Grenades. Even more difficult to aim than the grenade launcher. Pulse grenades are the notable exception, since they have such a huge area of effect that you don’t need to land close.
Miniguns. They look awesome, and have high DPS, but perform poorly against armored opponents, and are very heavy. They’re iffy in VATS, since their AP cost is high. When you fire them manually, they take a while to spin up, so you really only want to use one if you have a lot of close, unarmored targets to take down in a hurry. You can pick one up very early in poor repair, which you can remedy with Weapon Repair Kits, but generally the “horde of zerglings” situation just doesn’t arise - when you’ve got lots of targets, they’re often things like well-armored Legion troops.
Missile Launchers / Fat Boys. These are very situational, you’ll almost certainly miss, so you need a target where a near miss counts as a hit. So, shoot from above, or where the target is next to a wall, and don’t fire one off indoors. I got a fair amount of use out of these in FO3, but not in New Vegas. I just didn’t get as many opportunities, probably because the environment is less urban, so it’s harder to get elevation on your targets.
If you found the any of the above useful at Very Hard, particularly shotguns, I’d like to hear how, provided you can break down why a conventional pistol or rifle couldn’t do the same job more easily.
As an example of my own, I found the Silenced .22 hard to use when I first played. It has low DAM, and it seems like it’s not going to kill anything on Very Hard. Yet this last playthrough I found it deadly at low levels taking down thugs in the Bison Steve. With hollow point ammo it can one-shot stuff even at Very Hard provided you shoot your target in the head. The main secrets are that you must be undetected, and you really must aim manually. VATS won’t give you good odds at the ranges where sneaking is practical at low levels. Eventually your opponents get too tough, but below level 6 or so it’s a good weapon.