I think they are in quite the opposite ends of Linux desktop distro spectrum. Mint attempts to provide nice out-of-the-box experience and Arch is "tweak everything". Mint being based (more or less directly) on Debian includes far more distro-specific patches than Arch which has fairly vanilla packages (afaik).

As for my recommendation, imho you should learn the system you are going to use. If you want to learn Debian, use Debian (or Mint, or some other close Debian derivate). If you want to learn Arch, then use Arch. Every major distro can be poked and prodded, tweaked to no end, and you can look what happens under the hood.

Arch will give you a deeper view than Mint, including having to make choices for yourself, about every component you wish to use.