I use both. I find Bitbucket just lacks polish— it's hard to come up with specific examples, but various things give off the vibe of it being maintained by a small team within a larger organization for whom it's not really a priority.

Code search is one, but I also find it harder to get to the exact diff or pull request that I want. I don't get Github's nice rendering of filetypes like STLs, and there's a lot less of the context-sensitive popups when you're mentioning users, issues, commits, etc.

Bitbucket's issue tracker is kind of limited from ever getting too good, because it's really just there as a teaser for JIRA.