A custom domain can be added by creating a CNAME file with the necessary domain in the root of the repository and adding/changing corresponding DNS entries.
Low cache expires - GitHub sets the cache-control: max-age header to 600 seconds, or ten minutes. Normally, you would set this value to a year so that it stays cached, and then use fingerprinting on your assets. Instead of serving style.css, you would serve something like style-62c887ea7cf54e743ecf3ce6c62a4ed6.css. As it stands now, assets are rarely going to be cached on repeat visits.
This will give a low score on https://developers.google.com/speed/pagespeed/insights with a 'should fix' recommendation around 'Leverage browser caching'.
For a high traffic site this may have implications
A simple, blog-aware static site generator, Jekyll makes it easy to create site-wide headers and footers without having to copy them across every page. It also offers some other advanced templating features.
Due to GitHub's DDoS mitigation technology, users who host their static websites on their servers, cannot have a custom root domain. For example: "example.com" cannot be used, "www.example.com" must be used instead. While in theory the first one is allowed, it greatly affects loading times.
One of GitHub's features is a very powerful web editor which helps users edit or even create files right from the web browser, once the file is saved it's the same as a commit. Coupled with pages, this tool becomes even more powerful, giving users a free CMS that is easy to use and create.
BitBucket allows users to have free private repositories as long as it's a team smaller than 5 that is working on a project. In other words, BitBucket charges per team member and not per repository member. This feature may make BitBucket, even BitBucket pages better than for example GitHub for some, since the static page's source code won't be open source, but it can still be viewed on the browser, so for static page hosting per se it is not a big deal.
While GitHub's UI is extremely simple to understand and very polished, BitBucket lacks a bit on this category. With a design that seems old and not as pleasant to look at.