Simply , Both GitHub and BitBucket offer their best support .They are a bit slightly different depending upon their offer plans and price plans .
Some of their differences are given below :-
1) Github provides you inline editing and network graphs whereas bitbucket doesn’t provide you that.
2) Github’s monthly price is cheap, but bitbucket is cheaper than Github.
3) Github doesn’t provide any free private repositories whereas Bitbucket provides you unlimited free private repositories.
4) UI tool in both (not for people who love console 🙂 ).
Those two are quite alike. Bitbucket was released few months after release of Github , so many people blame it in plagiarism. May be they are correct or may be not, you can find a lot of discussion upon this.
Github has more users than Bitbucket, but my choice – both !!
I use Github for social network functionality, keep my all public repositories there, but when it about some private work I use Bitbucket.
Depending upon what type of project you are doing and what features you need ,I suggest you to choose the best one for you.