Linux Mint prioritizes elegance and user-friendliness, and is more open to proprietary software being pre-installed. However, I think the main difference is the default user interface:
-) Linux Mint: MATE (fork of Gnome 2) or Cinnamon (fork of Gnome Shell). KDE and Xfce variants also available.
-) Ubuntu: Unity
In my experience, since Ubuntu move into the Unity interface, I found more difficult to work in an efficient way. Ubuntu, as it is now, is more oriented for non-academic user, with a beautiful interface, which is perfect for looking at photos, videos, internet, etc, but is not so efficient for handling hundreds of files.
I haven't had a look at Ubuntu since two years, but I know that the Unity interface is much more stable now than before. However, I feel really comfortable with Linux Mint, in particular with the Mate user interface, which allows me to use some old PCs that are not capable to run the latest versions of Ubuntu.
Mint follows a Windows-like desktop distribution. This makes it easier for new Linux users. It also includes by default some applications and libraries that are better for most users (but they are not always open)
Beyond that, I think Ubuntu (+Unity) is now an excelent choice. It is very mature and stable, and as light as Mint (+Cinnamon). I have tested with +20 users (all newbies) and they have all adapted very well.