Unlike the previous release, Mint 16 installs its EFI boot files in a directory called ubuntu. This makes it difficult to install both Mint 16 and Ubuntu on the same UEFI boot systems. It’s not impossible, but if you aren’t very familiar with UEFI boot installation and configuration, I would recommend that you simply avoid this problem, and install only one of these two. Hint: I have a LOT of experience with multibooting UEFI systems, and trying to do it is enough trouble, and sufficiently error-prone, that I am not going to bother with it in this case.