Project and individual preferences are pretty much what drives us to use various version control systems. Mercurial and Git are similar, but I prefer Git because I use it daily and the people I collaborate with use it. I've seen companies use both systems, and Google has built their own internal version control system in addition to using Git for open source projects. The point I was trying to make was to use a version control system that works well for code. I don't think it matters which one, but as long as there is one that does a good job, that's what matters. Whether you use Git or Mercurial shouldn't matter. They are both better than Dropbox or Google Drive for code.
However, I think that Dan was just asking about using something that is easy to use with a high turnover of students. I'd suggest using Google Drive because you can modify and store all of your documents online and will be able to do everything in the browser.