I do not fully understand the difference between Debian and Ubuntu based. What arr the advantages? What arr the differences? What are the disadvantages?
LMDE has a smaller memory footprint than Linux Mint 13, but can't use the Ubuntu based PPAs, and operates more like Debian Testing than Ubuntu does. If you want
Unity, it is simpler if you stay with Mint 13, which is Ubuntu based. LMDE is an 'install once, then do incremental updates.' Linux Mint has regular updates which require major updates about every 6 months, as the parent Ubuntu does.
CentOS/Fedora/RedHat Enterprise Linux (a.k.a. RHEL) use rpm (RedHat Package Manager), while Debian uses apt-get, aptitude, or Synaptic as a package manager (basically 3 ways of accessing the same manager), and from the desktop, can use the Ubuntu Software Manager. There are also differences in the kernel hardware support, minor differences in system folder usage, and other differences in setup, virtual machine management, etc. Debian and RHEL both only release when ready rather than on a fixed schedule as Ubuntu/regular Mind does, and thus can have several years between stable releases. Both will also have older desktop applications than the latest Ubuntu/Linux Mint, because the application version is frozen at the time of the stable release and only receive security and stability updates.
LMDE is called a 'semi-rolling release' in that you install once and the default installation tracks the Debian Testing repositories, not Debian Stable or Old-Stable. LMDE also has many tweaks by the Mint team to make LMDE look and operate more like Linux Mint standard version.