Download them both, burn to a USB or disc, and run in Live Mode (or use a virtual machine). That's just one advantage of Linux over Windows: you get to try before you buy.
The one you enjoy most will likely come down to personal preference; in my experience they're about on par when it comes to resource usage and stability, so if you like Unity you'll gravitate toward Ubuntu, while if Cinnamon suits your work flow better it'll be Mint.
A few key differences between the two:
Ubuntu comes with Unity by default, while Mint is pushing Cinnamon and MATE as it's two primary desktops. If considering Mint I'd look at Cinnamon over MATE, as Cinnamon is developed by Mint "in-house" and is now considered the distro's defining feature.
Ubuntu ships with less apps than Mint, though it still covers all the bases. Mint comes with Flash and media codecs which in Ubuntu must be enabled by the end user. Mint also has it's own Update Manager, one notable feature of which is a 1-5 rating system applied to all updates; only level 1-3 will appear in the Update Manager by default, while packages deemed "risky" (like kernel updates) are held back from the user. Ubuntu's updater gives you everything...good, bad, and ugly.
Ubuntu's direction is strongly dictated by Canonical, while Mint's lead developer Clem is much more focused on what the community asks for; the development of Cinnamon largely derived from a user base not happy with either Unity or GNOME 3.
Remember that Ubuntu and Mint both share a common software repository, so if you like some of the applications Mint ships by default (Pidgin, VLC, Tomboy, Banshee) but prefer Ubuntu's Unity interface, you can always install them on Ubuntu via the Software Center.