If you’ve used and like GitHub Pages, and are just going to host a website as quickly as possible, it’s probably going to be the better option for you. GitHub can host the website, and GitHub Pages has better documentation and support than MarkdownSite does. MarkdownSite would likely be the bad choice right now for this. It launched literally last night, and I am hoping to get enough traffic and feedback from people playing with it so I can see where I can improve it.
If you want to run your own version of GitHub Pages, and host the website on virtual machines or bare metal servers in a data center, and to then provide that hosting to others, I don’t believe GitHub Pages has any self hosting option that I could see. If that’s true, MarkdownSite would be the better option in that situation.
On a personal note, it is perhaps an incredibly self-indulgent project in that I’ve always simply liked web hosting technology. I want to share that by creating and running a hosting platform myself, and to have the code and documentation and network diagrams out in the open for it so anyone else can run their own too.
I hope this helps explain some of the rational, thanks for checking it out!