Another way to compare tools: is it possible to transfer full history?

I have seen lots of comparisons between source control tools, but have not found a comparison that would explain the fundamental differences and similarities in a way that would really let me choose. So I decided to try a new approach: if one tries to transfer the full history of an application or a larger product/project, which features can I rely on finding in any decently recent tool?

Let's start from Git vs. Mercurial: is it possible to move the whole history of an application (with or without submodules) from Git to Mercurial? From Mercurial to Git? If it is not always possible, what is the feature that might completely prevent the whole attempt? If partial transfer is possible, what information might be missing in the result?

I am not interested in whether it is easy or fast in practice. I am only interested in the concepts and finding equivalent classes for the tools or at least their core concepts.