I don't really have a favorite manufacturer in BL3. Just favorite specific weapons. I look at dps, basically.
Like, there's this shotgun The Lob. Fires a giant ball that is super slow moving. Normally you'd toss it thinking "useless." But lvl 57 ones do around 11k+ elemental damage. So I put it on and charge into enemies faces and fire so they can't dodge. Boom, often a critical and they're dead - thus I like the weapon even if initially it seems like it "sucks".
I love high elemental and splash damage. Especially in Mayhem 3+. I am a charge into the middle of a fight type, no stealth, I (mostly) gave up on snipers and any subtlety since BL2 (sniping was the bomb in BL1 tho). Hubby's still the more subtle type, using cover and trying for precise shots and the like (he takes 3x as long to do/clear anything, I swear, heh) but eh, not my style anymore. So I choose gear accordingly.
Edit: My current favorite weapons are Hellshock pistol and Yellowcake. I typically need nothing else, really. I can blow through storymode/normal through all of Eden6 using a lvl 14 Hellshock. >.> Lydia sniper can be awesome too. Note: power wise, almost anything works on Mayhem 1, don't have to be picky there and you still get plenty of Legendaries in M1. Hubby sticks to that.