As someone who has used both as my primary operating system the main reason I ended up on Arch is the Arch User Repository (AUR).
The AUR allows you to run installation scripts for apps that aren’t supported by the official repositories and pretty much everything you could ever want is there.
The other big thing I liked is the Arch Wiki documents everything really well, and I preferred the kinds of answers I found there and on the Arch forums to the Ubuntu/Mint forums.
At the time, operating system overhead was extremely important to me and a window manager like i3 or awesome was less resource intensive than Mint’s Cinnamon Desktop Environment (DE).
All of that being said though, because Arch doesn’t ship with a DE getting started will require a configuring a lot of things using old school text based configuration files. The Mint installed on the other hand leaves you with a very capable and functional system as soon as you finish installing it.
If you want something that works right out of the box, I would recommend Mint. If you want a project give Arch a shot!