LMDE will generally be a tad faster as Debian is a more lean base system as compared to Ubuntu. Downside is you lose compatibility with Ubuntu. If you need additional programs, or newer version of them, on Ubuntu you can usually find a PPA from the developer with that. While you could theoretically use a PPA also on Debian, because of difference between Ubuntu and Debian base that's not recommend and might cause problems on your system. Ubuntu base might also support a tad more hardware devices and peripherals. If not of that is relevant for you, LMDE might be a good fit.
I'd say it does require you to be a bit more of a responsible citizen, and keep an eye on the testing ongoing for a next update pack in the Update Packs Repositories > Linux Mint Debian Incoming
forum so you know what issues you might run in to during upgrade and how to solve them. Like for UP#7 there was this topic: viewtopic.php?t=144198
. UP#8 is coming up next and a similar topic will be started in that forum for that.
To clarify; LMDE has basically three repositories:
- The Linux Mint repository where software added by Linux Mint is kept (Cinnamon, MATE, Firefox, Thunderbird, etc): http://packages.linuxmint.com/list.php?release=Debian
- The "incoming" repository, where a few times per year upgrades from Debian testing repository are copied to and then tested for a month or so by the Linux Mint developers and interested users from the community. Users will post workarounds and solutions for issues they find, and for some issues upgrade/downgrade of packages might be done by the Linux Mint developers to fix problems.
- The "latest" repository, which is basically a copy of the "incoming" repository after it is deemed stable enough for all users.
By default you'll have the Linux Mint repository and "lastest".
It's good to be aware that you can get upgrades through the Linux Mint repository at any time that the Linux Mint developers do upgrades there. You will only be getting upgrades for the "latest" repository when a new update pack is done (with except of security updates I believe). It's also good to understand what Debian testing repository is, and that this doesn't mean you will be running bleeding-edge versions of programs.