Regarding your second comment, you do not need to host your own instance if you don't want that.
You can host all your repos, public and private, for free at Gitlab.com. There are no limits, besides a 10GB limit for git annex and no restrictions to its usage.
If you're avoiding servers, that also means that you have different accounts for every SaaS service replacement you use, and administering permissions and accounts means a lot of extra and pointless labor.
Using custom code to facilitate your business' processes -- such as server-side plugins for things like your source control -- becomes impossible.
Business processes become dependent on SaaS + data dependence that can't easily be exported from the SaaS services, and you're paying out the nose for them every month -- locally licensed software is cheaper, for quite obvious reasons, all across the board.
All so that you can avoid a once-in-N years failure of a hard drive and running apt-get?
No thanks. That's an insane cost/benefit analysis.
Server administration should be easier than it is, but it's not hard, and I'm not about to make every other business process worse just to avoid it.
* No private repo in the free plan
* Pricing per repo in the paid plan - probably fine for a startup with just a couple products, unusable for a service company that starts a new project every month
So if you care about private repos, BitBucket vs GitLab is interesting.
I think GitLab is great, but still prefer GitHub: no need to worry about hardware failures, or management. Someone does that for me, and does it well.