The only run advantage a Barb has terms of speed is a few points in Increased Speed.
As for their slow, if you're both slowed the same amount, the duel pretty much evens out again, which leaves you were you began, ww vs smite. And WW > Smite.
I did say that WWsins dont cut it in BM vs a smiter, but why bother slowing the Sin down when you can just Deaths + Andys + Antidote their damage to nothing anyway? Even a 6k WWsin (no mobility though, because it needs bramble) wont do enough damage to overcome that.