Both are very good distros. And both use the Debian package manager method to do the work of installing and deleting packages. One has the option of using either a terminal or the GUI (Synaptic) version to do the work. I love Debian based distros. It so darn easy to mange your Linux OS. It really is.
As to the two you mentioned, Ubuntu is a great distro and easy to tweak. It prompts you when needed. Lots and lots of forum support. But for my money, Linux Mint is top notch especially for anyone new to Linux. While you'll have to install certain things in Ubuntu - which it will prompt you to do - Mint has it all. Very little to add to it. Truly one of the few 'works out of the box' distro out there.
Now if you really want to get geeky, try the granddaddy all Debian distros are based on - Why Debian, of course. A bit more work and hair pulling and gnashing of teeth to do. But not all that much more. Of course it's the package manager that makes all this possible. Just can't beat the Debain package manager. Bar none! EX: Via the terminal, 'apt-get install package'. apt-get delete package'. Of course the GUI (Synaptic) is just a matter of point and click. I'm currently using Mepis on my HP laptop. Another Debian based distro worthy of your consideration.
And while I'm at it, download/install packages designed and provided for the Linux you are using. Stay away from those nasty tarballs. Ugh!
Visit Distrowatch for a listing of just about all the distros available - hundreds!. From the most popular to the most obscure one man operations. distrowatch.com