I would take Barnett by tko.
Josh has proven that he has a good chin, I don't think you can say the same for Mir. Josh also is game in the later rounds, where you don't see Frank go 3+ rounds very often. He has the better wrestling too. Grappling wise they are even, but Barnett would be the one getting the takedowns and I don't see him getting subbed from guard so...I see him stopping Mir within 3.