When we were making the decision at my company, we went with Github because the dev team cared about having the little green squares show up on the "activity" chart for their account's... I know, petty, but it's something, and since most of us do FOSS projects, it's a status thing.
It used to be any commit that made it into a repo's master branch, the green squares showed up, even if it was a private repo (it just didn't show details of the repo to public users). But now, those don't show up to the public, only the user themselves sees them while logged in... so if we were making the decision today, I'd probably lean towards Bitbucket.