With Mint it's not a problem to use applications from an Ubuntu ppa. With LMDE it doesn't always work.
In general, LMDE is not updated as often as mint.
Lot's of developers tend to target Ubuntu as the default Linux environment so if you're lokking for a windows like experience (downloading packages from the developers website instead of using the repositories) Mint will probably be a better fit for you.
On the other hand, if you prefer something more customisable, and can handle the occasional hiccup. LMDE is quite rewarding. It gives a great opportunity to really understand how the system works.
short version: LMDE if you want to know how your computer works. Mint if you don't, or want to use ppas.