I like Karl's "equation"...that is an excellent way to summarize it
Actually this equation simplifies things a bit, hm, maybe a lot.
The difference between Ubuntu 13.04 Unity desktop and Mint 15 Cinnamon desktop is not only the desktop environment:
+ Mint uses mdm instead of lightdm.
+ Mint by default does not make use of compiz.
+ Mint uses a lot of forked Gnome3 programme modules.
So some of us are pretty well aware that turning Ubuntu into Mint requires more modifications than just replacing one single software package Unity by one single software package Cinnamon.
Cf. e.g. here: [HOW TO] Convert Ubuntu 12.04 to Linux Mint 13
Yet, the central and most visible difference between genuine Ubuntu and Mint is the desktop environment, the user interface.
This is why from my point of view going back from a Mint desktop environment (Mate, Cinnamon) to the default Ubuntu Unity desktop environment you are reverting Mint back into Ubuntu. This is why from my perspective the easiest way of getting the Unity desktop is by installing genuine Ubuntu 13.04 with the Unity desktop directly.
Yet, as mentioned in a previous post, not all users share my point of view and installing Unity on Mint is feasible: unity on maya