Bitbucket supports kanban boards today. Checkout our integrations page [0]. Two of our partners Comalatech [1] and Transition Technologies SA [2] both built simple solutions that display your Bitbucket issues in a kanban board.
Full disclosure: I'm Head of Product for Bitbucket. LMK if you want to chat, a link to my calendar is in my HN profile.
[0]: https://bitbucket.org/integrations/cloud [1]: https://marketplace.atlassian.com/plugins/com.comalatech.bit... [2]: https://marketplace.atlassian.com/plugins/bucketboard/cloud/...
Bitbucket engineer here. Not to derail, but since Bitbucket has been brought up a few times in this thread and we're talking differentiating features this seems relevant: Bitbucket also has native Docker-based CI/CD in the form of Bitbucket Pipelines[0].
What we hear most frequently a reason for switching is the in the integrated CI, CD, and container registry. The GitHub importer will import your repo, issues, PRs, milestones, labels, and wikis http://docs.gitlab.com/ce/workflow/importing/import_projects...