Bitbucket actually does many things better than GitHub. The pull requests, for example, are better in many small ways.
That said it's also buggy as hell, and Atlassian still haven't bothered to support git mv properly, so GitLab is something I plan to look into when I get time.
I've deployed a Gogs installation at home and am very happy with it. It's not Github, but it's great for my needs, and I can create accounts for friends to use privately, which is fantastic. I've tried GitLab and it is also very good.
I would have actually recommended GitLab! It has all the features of GitHub and more, and is actually open source (https://gitlab.com/gitlab-org/gitlab-ce/)