Really Linux Mint MATE isn't that much different from Ubuntu MATE -- the difference is mainly a different panel layout (by default) and some other tweaks here and there around the desktop. Most strikingly, there is a panel off to the left side with launchers much like what Unity used to have, and a panel at the bottom with a searchable applications menu. Basically the Mint MATE version is tweaked a bit to make it look more like a lightweight version of Cinnamon -- Cinnamon is primarily developed by the Mint people themselves, last I checked.
In other words, under the hood they're not very different, and user interface-wise they can be made to look extremely similar to each other. Heck, you can make MATE look a little like XFCE if you wanted to.
Basically you don't choose Mint MATE over Ubuntu MATE due to huge user interface differences -- you do so because there are other applications like software installation tools which are unique to Mint. That's mostly it. But this comes from a guy who used Mint only briefly, about three years ago, before realizing I didn't like it.