Sometimes I like my distro to "just work," and sometimes I wanna get in there and muck around a bit, and LMDE is the first distro I have used that seems ok with both "modes."
I use a different distro for myself, but I have my family running Mint (Ubuntu version) on their computer. It works well, because they can just use it without thinking about it, and I can handle all maintenance remotely.
They have incredibly basic needs, so I don't think they'd really notice the difference, but I'm curious where the differences lie - I installed the Ubuntu version without thinking much about it because it was the default (only?) version at the time.
Probably the biggest thing I like about debian-testing as opposed to ubuntu is the rolling releases. I really don't like the "run `do-release-upgrade` and cross your fingers" method of upgrading.
For the most part though, the ubuntu-backed version seemed to "fight" me when I would get into my "mucking-around" modes. I know, I know, it's all linux underneath, but I just find the debian version so much easier to customize.