I'm happy with KDE since 2009. But I'd have a really hard time if I were to choose between those two.
I think I "know" MATE because before KDE I used to use Gnome2 so it feels nostalgic to me. The Applications/Places/System menu was the tits and it beat the shit of whatever start menu you put in front of it, and Gnome's decision to get rid of it was the stupidest idea ever (among many other of their utterly stupid decisions). I'd really miss that menu if it weren't for that I got used to associate some keystrokes to launch my favorite apps so I don't even use a start menu or whatever, rather than Krunner.
On the con side it seems to me MATE is being developed at a slower pace than Xfce's, and it seems less customizable than it - well, at least for me that's a con - thought I'm not really a "ricer" or anything I just got used to a certain way to do things on the desktop and I remember having to fiddle with Gconf2 to do stuff like you did with friggin' Windows Registry editor.
I got to use Xfce back in the day too. It has an Applications/Places menu just so people wouldn't think they blatantly copied Gnome, but it's more than 10 years since Gnome got rid of it so I don't know why they haven't took it. Xfce feels somewhat more customizable, has the veteran badge and seems to have more developers backing it up.
But it's being developed with GTK+3/4 so I guess at some point they'll suffer from the ~~shittification~~Gnome-ization of GTK and, as I said before in some other post, if I were them I'd move all my shit to the E libraries (even more, I'd do a fusion of the Enlightenment desktop and Xfce). Also I happen to be a graphic designer so the lack of care they have onto some things sticks like a sore thumb to me, like those poorly designed settings dialogs on some stuff that even have some dumb horizontal scrolling just because they couldn't care less about that.