I'm currently evaluating options for Git repository hosting services for my team. I'm partial to using GitHub, but there may be reasons that we would instead (or in addition) want to use Atlassian's Stash.
With Git is it possible to copy a repository and its history from hosting service to another? Are there any gotchas with doing this? If we go down one provider and decide we have to switch later then is there anything that we would lose?
I am interested in the general answer about this for Git, but also are there any likely issues with data (not necessarily just source version history) stored as part of that would be lost by trying to migrate specifically between the GitHub and Atlassian stacks?