It's just that they are two different Desktop Enviroments. Like Gnome, KDE, XFCE etc.
Take a look at *mylinuxexplore.blogspot.in/2013/12/linux-mint-16-petra-cinnamon-and-mate.html and *forums.linuxmint.com/viewtopic.php?f=60&t=135464 for exact differences and advantages / disadvantages.
Though always remember that, DE is always personal choice and it may not suit you depending on other's opinion.