Bad Brains no doubt; the originators to the fullest! Everything that they put out is on hit, even when Joseph I was singing with them. I like Living Colour too, but the only good album that they put out was "Time's Up" Oh yeah, and even H.R's (w/Earl) solo albums is on point too.
If you put both bands together in their prime--and I'm old enough to have caught both at their best--the Bad Brains would kick Living Colour's collective ass. If you're talking about pure musicianship, to a man Living Colour is probably better. But in terms of the whole package--musicianship, lyrical message (there was so much conscious black stuff in their lyrics it's not even funny), stage show (in terms of stage show, only Angelo Moore of Fishbone could equal HR back in his prime, you'd hardly know the lethagic old man on stage now was once a maniac of a frontman), and again I'm speaking if we're looking at both bands at the top of their game...without a doubt it would have to be the 'Brains. They're also a much more influential band, you'll hear more bands say they were influenced by the 'Brains than you will Living Colour.