I did. Some customers of mine use it (free tier if possible) for their private projects. My assesment:
* issue management is better than GitHub's one but for very simple needs (90% of the repositories?) GitHub is enough and BitBucket is needlessly complicated (don't even talk about Jira).
* repository navigation is worse (finding the repositories themselves can be difficult if you land on the wrong page)
* wiki/pages are probably the same
* access control and general management is better
* pull request... I don't know. Our teams are small and normal communication plus git merge are enough.
We use BitBucket extensively at my company for two reasons: Mercurial support and Unlimited private repositories.
The mercurial support is great because of legacy code (I finally have come to admit that Git is superior for most purposes). The unlimited private repositories is great because we make loads of projects. I came from so many companies that would have this giant monolithic tree of tangled dependencies because they would check everything into one project. I fear this with GitHub's pricing model.
I find BitBucket's dashboard useless. It used to be decent but they changed it some years back. BitBucket's security was sort of disturbing as well but I believe they have added 2 factor authentication.
I will say that Atlassian's Jira used to be the best bug tracking but I have found that in the last couple of years it has become a complete bloated pig that is overly complex and slow. The hosted Jira is so awful that we contemplated just using BitBucket for bugs. We eventually switched to Youtrack and are loving it.
I use it for personal, small scale repos where i just want to have the repo online and available across machines. Having the free, hosted tier is invaluable to me as a single developer.
That said, I've also used it in a paid, hosted environment supporting a team of 10. Again, our needs weren't overly complex and the integration with team software like Jira and Confluence were great (as can be I suppose, given the complexity of both tools).
I'm actually surprised there isn't more of a discussion around bitbucket and the cost of hosting smaller, private repos. Do most just dislike bitbucket or are you hosting bigger projects with multiple contributors which requires Github / gitlab services?