Bitbucket vs. GitHub: Which project host has the most?
The right choice boils down to a number of factors -- you might even consider using both
Project tracking integration
This is less a feature of Bitbucket or GitHub than of the project tracking software you use. It's worth mentioning, though, because good integration is fantastic and timesaving. First look to see if your project management software integrates with either. If it does, check out the features and weigh them against one another.
A basic integration would simply be linking changes to bugs or development tasks. Many project trackers go beyond that, providing luxury features (and after using these features, they do feel luxurious), like the ability to change the status of an issue or to log time to an issue from within a commit message.
We use Jira, which has support for both GitHub and Bitbucket, so that didn't narrow our search. If you use a different project tracking solution, do some research and see if it narrows yours.
Nobody wants another set of login credentials, right? In the current climate, many apps will let you authenticate via your OAuth2 provider of choice. Unfortunately, GitHub doesn't allow for external authentication. Each member of your team will have to set up a new account at GitHub. Bitbucket, on the other hand, allows you to log in with Twitter, Google, Facebook, OpenID, and GitHub (oh my!) credentials. This point isn't critical, but it's definitely worth considering.
When we migrated to the cloud, one of our decision points for services was how you log in. In our case, we were adopting many new services and didn't want to deal with having to manage a ton of new credentials. Since we had already decided on Google for mail and other apps, we chose a set of services that met all of our needs and would allow for authentication via Google. This wasn't possible for every service we have, but I can log into most of them with a single account.
It's not a make-or-break feature, but single sign-on means fewer headaches for your developers, less time spent on lost password requests, and more productive hours.