You know, the time required to host Gittea (or Gogs) is basically nil (you'll have to set your environment up for Github too). And by maintaining it, you mean making sure it's online and taking backups? Because I don't see how you can save any time on those by using Github.

Where you host it is of less relevance, because you can simply take your backup and server script and run them at any different provider any time you want.