Bitbucket has unlimited private repos. In the case you wish to go public, obviously Github has a larger community, but it's also easy to just uncheck the 'private' box in Bitbucket.
So why has Github been the place to-go for hosting code?
[1]: https://en.wikipedia.org/wiki/Unix_philosophy, not that's objectively better, just that in this case it seems to provide an advantage.
[2]: When I signed up several years ago, I think it was only five private repositories...and Mercurial was favored over Git in the signup process. But free private repositories was why I chose Bitbucket over Github. I was using it for Coursera assignments.
[3]: Github versus Bitbucket may also be explained by Zawinski's Law: The yang to it's Unix philosophy yin. http://www.catb.org/jargon/html/Z/Zawinskis-Law.html
1. Github got First Mover momentum
2. Git preference over mercurial back when Bitbucket burst on the scene.
3. Github has many users which means its easier if you want to reach a large audience with your FOSS project.
4. Due to #3 large companies hosting all their big projects on GH, leads to a self perpetuating cycle.
Maybe it's the network effect.
Nowadays, I like the ui, responsiveness and developer interactions provided by github. I don't like Bitbucket's color scheme and sometimes it's slow.
We have a hosted instance at work (CE), and I've fallen in love with it. So I decided to put my personal stuff on Gitlab.com. All my new personal projects have been hosted there for the past year or so. Also helps that you can keep them private.
The major advantage of Github that I see is the network effect.
Docs: https://docs.gitlab.com/ee/workflow/repository_mirroring.htm...
People don't use it because they are hipsters they use because it works well.
I use gitlab (and to a lesser extent github) at work now and IMO gitlab vs github they are about equal in terms of ease of use and "just working like you expect."