Recently had a need for something like this and Gitlab ended up losing to BitBucket Server which we bought along with JIRA and Confluence. Gitlab seems like a nice, light solution, but their issue tracker ain't JIRA.
My company is using atlassian products heavily and I was surprised to find very good support for GitLab. I run it locally and love it and I'm pushing to use it at work.
It's worthwhile noting that the integration between JIRA and Bitbucket (naturally) goes far beyond adding comments with links to a ticket.
Our aim was to provide an at the glance view of the development status (# of commits, branches, pull requests and their status, builds and deployments) with the option to see more detailed information right within JIRA. And of course you can create a new branch right from your JIRA issue.
Lastly, ensuring that the data is 100% reliable and up to date was an important consideration which most of the basic webhook integrations simply ignore.
No doubt, that said I've used both before and I generally prefer GitLab to bitbucket and so as long as the basics work I'm happy. Also GitLab can satisfy both Bitbucket and Bamboo and since my company needs to host all apps it's MUCH cheaper to use GitLab than to pay for 2 more tools for all developers.
