I like to think of Github as Facebook, Bitbucket as Google+. I use Bitbucket all the time (and love it), but it doesn't have the social network for whatever reason.
Agreed. I also think that Mercurial is really great, and I'd recommend that anyone who has only used Git spend some time working with Mercurial instead.
It seems to me that Git has won the popularity war,and GitHub has benefitted from that. GH has also focused on the social networking side more.
As an academic, I'd recommend BitBucket, and pretty much every academic I know prefers it to GitHub due to the free academic accounts.
To students preparing for graduation, I'd recommend getting a portfolio together on GitHub, but also spending time on Mercurial - it is much nicer in some ways, and variety is good for the soul.
Maybe you are on to something here. I am a g+ user, but not Facebook. I don't care about the social aspects of my code at all. Almost all of it is closed source anyway.