HMGs and especially miniguns are pretty great against armor because they strip it with every hit, and fire a lot (especially miniguns). HMGs also just do a lot of damage and are surprisingly accurate when crouched.
In my first playthrough I used slugthrowers a lot against armor due to high damage, but their low rate of fire hurts them. Using chem rounds can strip a lot of armor, though. Chem grenades are probably great anti-armor, though they probably target under-armor most of the time so explosives are the best followup.
Plasma also strips armor and can cause burns. It's relatively hard to get, except for the "Killer Bee" (used to be Hornet I think?) sold by Contacts: Smugglers. Only 3 shots, but it's a compact and "affordable" emergency weapon. The I-gun does a bit less damage and is less accurate, but fires about twice as much... once you get Contacts: Authorized Dealers to buy the ammo.
The nice thing about "armor pre-damage" is that it strips armor even if it doesn't penetrate the armor. That's why the 30-round-burst minigun is so great, every hit is taking off at least a little armor.
Oh and melee weapons tends to do massive, relatively reliable damage in strong hands. The Spike Club is particularly good against armor, though it's concussive. For some enemies (like lobstermen *shudder*) you really want a slicin' sword instead.