Short bio: Computer Scientist, FOSS supporter (read more)
Tux Machines (TM)-specific
Few desktop environments have benefited from the recent diversity of interfaces more than Mate and Xfce.
A year ago, Mate hadn't even reached general release. However, since then, it has been influential in making Linux Mint the distribution of choice among experienced users. Similarly, after years of being the third most popular desktop environment, Xfce has become one of the major alternatives.
However, despite their similarities, which one is likely to appeal to you depends on what you are looking for in an interface.
Similar GNOME 2 Origins
The newfound popularity of the two desktops is explained largely by the fact that both are based on GNOME 2. Mate is a fork of GNOME 2, openly intended as an alternative for those dissatisfied with GNOME 3 and Ubuntu's Unity. Having spent several years consciously imitating it, Xfce also resembles GNOME 2, down to the wording of many menu items and dialog boxes.