(I'm going to refer to Bitbucket Server as Stash here because that's what it's been called for most of the time I've used it and to keep it distinct from the public offering I'm comparing it to.)
Stash and Bitbucket have converged more than I expected, mostly because my recollection of Bitbucket was closer to Github than it actually is. But versus Bitbucket, Stash is missing Mercurial support, snippets, issues, wiki, project overview pages, and some social features. The lack of snippets was particularly vexing to me in my day-to-day work until we started using Slack. And Slack snippets are still a poor substitute for Gists.
Versus Github, the difference is more pronounced. Github has better search (and it isn't even that good), much nicer pull requests with superior integration to the issue tracking system, a much better API, better profile pages, static site generation, and in-place editing.
Yes, I know the answer to the lack of some of those features is "use our other products too", but Atlassian's competitors offer products with lightweight issue tracking and wikis. And while the features Stash provides are generally decently implemented and usable (the last few versions have been a big improvement), Confluence... is poorly suited to be used as a programmers' wiki, to use the gentlest language I can muster.