Install number one: LMDE 201303.  I was hoping for the best of both worlds, but I got driver issues instead.  LMDE has known ATI proprietary driver install issues.  I followed the Mint instructions and got it working, then got a blank screen after too much tinkering.  I was surprised that LMDE had this problem since Debian doesn’t, and LMDE should be a more polished version of LMDE.  This wasn’t a big deal, but I decided to give Debian a chance.
Install number two: debian stable (7.3).  The debian website has a convoluted maze of installation links, but it’s still fairly easy to find an ISO for the stable version you need.  I installed from the live ISO using a USB key.  The installation and ATI driver update went smoothly, and I thought all was well at first.  I soon realized that about 50% of reboots failed; the audio driver was the culprit.  I installed the latest driver from Realtec/ALSA and it sort of worked, but I was still getting some crap from # dmesg and the audio would crackle with some files.
LMDE. Â I live booted LMDE to see if the same issue existed there and it did.
Time for Mint 16.  As expected everything worked.  Man I really wish Ubuntu hadn’t chosen the dark side – their OS is really good.  All of these distros use ALSA audio drivers, so why is Ubuntu the only one that works?   Kernel versions:
debian stable (7.3):
cat /proc/asound/version
Advanced Linux Sound Architecture Driver Version 1.0.24.
Mint 16:
cat /proc/asound/version
Advanced Linux Sound Architecture Driver Version k3.11.0-12-generic.
One more thing to check.  What kernel version is the real debian testing “jessie†using:
http://packages.debian.org/testing/kernel/linux-image-3.12-1-amd64
LMDE 201303 = 3.2
debian stable 7.3 = 3.2
Mint 16 = 3.11
debian testing “jessie - Jan 2014†= 3.12!
I determined to try debian testing before settling for Mint.  I tried a netinstall from USB key which killed my PC and grub bootloader.  The debian stable live iso usb key decided to stop working as well.   I finally got a real DVD debian stable install to work, changed the repositories to point to “jessie†and upgraded.  I was very surprised to see this worked!   I’m having some problems with bash, but all of my day to day software is up and running.  Nice.
TL;DR: LMDE was using an old kernel so I needed the real debian testing (jessie) to solve my driver problems.
Which issues are you having?