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.
As a result, both Mate and Xfce can be classified as traditional desktops. They consist of a desktop display, a panel and a launcher, and both are largely free of 3-D effects, the influence of mobile devices or any effort to innovate in any major design elements. Contrariwise, each includes the technically useless screen-saver, presumably in keeping with tradition and users' expectations.
Each is an obvious example of the type of interface that was introduced in the mid-1990s, and remained dominant until the last four years.
However, the aims of Mate and Xfce differ strongly, to judge from each project's home page. Mate proclaims itself "the traditional desktop environment," and so far its developers have sought to do little else than to continue to make a popular desktop environment easily available.
By contrast, Xfce's home page summarizes the desktop environment as "fast and low on system resources, while still being visually appealing and user friendly." Like Mate, Xfce generally lives up to its self-description.
In addition, Xfce still shows signs of its more geeky past. The project only added user-friendliness as its goal around 2006. Even a few years after that, Xfce hadn't completed the simple, user-friendly task of adding a desktop launcher.
Instead, for the first year of its existence, Xfce emphasized speed and a small footprint. Evidence of these priorities lingers even now in the interface's inconsistencies and the tendency towards buttons and lists in dialogs and configuration settings. One or two dialogs, such as the Setting Editor might still seem formidable to less experienced users. So might the file manager's option to "Open Parents."
Nor has Xfce spent as much time as modern alternatives like Unity have in worrying about such details as rounded-corners or the width of scroll and slider bars. Despite the introduction of user-friendliness as an equal goal, to this day Xfce tends to have a blocky, slightly awkward appearance.
By contrast, Mate draws upon a decade of incremental development for GNOME 2. If it is less consistent and less current than modern desktop environments, it is still more consistent and less old-fashioned in appearance than Xfce.
At the same time, if Mate is faster than GNOME 3, it is less responsive than Xfce in every way imaginable, from start time to the speed with which windows open and shut.
But these generalities are only part of the story. There may be individual features scattered through both desktop environments that influence your choice as well.
Desktop, Panels and Menu
The Xfce and Mate desktops have a generic similarity. Broadly speaking, they share the same features. Sometimes, too, they share the same missing features, or perhaps the same assumptions, as when both allow you only to arrange desktop launchers automatically in columns from top to bottom.
However, if any general description of differences can be made, it is that Xfce tends to have a more minimalist feature set, while Mate has more options.
For example, both have a classical menu, with sub-menus spilling out across the desktop. Both menus, too, allow you to drag and drop items from the menu to the desktop. However, while Mate has the full traditional GNOME top-level menus of Applications, Places and System, Xfce defaults to Applications alone. If you want the other two top-level menus, you have to add them via panel applets.
Nor does Xfce come with a menu editor, the way that Mate does. Moreover, while its file manager Thunar is clearly inspired by GNOME 2's Nautilus, Mate's Nautilus has more options for configuring how contents are displayed. And while Xfce does include notifications, each one opens staggered down the desktop, creating a temporary clutter that Mate and other recent desktop environments have struggled to contain with varying degrees of success.
In other places, Xfce and Mate each have features that the other lacks. Xfce, for example, allows you to shorten the length of panels, while Mate does not.
Another example is the panel clocks. Mate's is unique in offering settings for multiple locations and offering weather reports, while Xfce, inspired by the variety of clocks that GNOME 2 once offered, includes the choice of Analog, Binary, Digital, Fuzzy and LCD clocks.
Occasionally, too, Xfce can be much more thorough than Mate. To give just one illustration, both have context menus from which you can add icons and change the desktop wallpaper. However, Xfce's context menu includes a link for opening a terminal, as well as a complete copy of the main menu -- tools that seem another legacy of Xfce's geeky past.
Xfce can also surprise you with features like custom actions in the file manager
Such differences might matter immensely if you are a compulsive customizer, or not at all if you tend to accept your desktop environment the way you find it. But, whatever the case, you might want to draw up a list of must-have features and see which one has the most of them. Probably neither will have all of them, unless you're very lucky.
Apps and Panel Applets
One of the reasons that GNOME remains popular in one form or another is that, over the years, it has accumulated a web of applications that take advantage of GNOME's features. Among the desktop environments, only KDE can compare.
Mate can take full advantage of this ecosystem of applications. In comparison, Xfce's native applications are few fewer and less impressive. They include a DVD burner, a mixer, an application finder, a calendar and a virtual terminal. These apps can only be described as functional at best, and as lacking anything extra at worst. Admittedly, Xfce's Midori Web browser shows some promise as a lightweight alternative, but many distributions do not even bother loading it by default -- including Xubuntu, which is probably Xfce's most widely used variation.
Fortunately, Xfce compensates for this lack by running GNOME apps almost as well as GNOME itself. In theory, GNOME apps probably run slower under Xfce, but because Xfce is generally faster, you are unlikely to notice the difference. Unfortunately, the same is far from true of KDE applications, which can take 15-20 seconds to open.
The exception is the panel apps, the small bits of functionality that can do so much to customize a desktop. Mate inherits GNOME 2's unimaginative set of panel applets that is chiefly a combination of basic widgets such as taskbars and system monitors. Admittedly, Xfce's collection includes many similar items but is enhanced by such useful options as the self-explanatory Directory Menu and Screenshot.
In configuration tools, Mate and Xfce have a rough parity -- a fact that is not immediately obvious because of differences in how the features are grouped and named. The main difference is that Mate opts for separate configuration applications, grouped in the top-level System menu under the Preferences and Administration sub-menus, while Xfce's Setting Manager (one of the few thoroughly modern interfaces in Xfce) consists of icons grouped into several categories.
Making a Choice
At times, choosing between Mate and Xfce is a matter of selecting between nuances. In these circumstances, the question you should ask yourself is, "What can't I live without?"
Many times, making a choice means deciding what matters to you. On the one hand, if you want a more modern desktop, with a complete collection of native applications, Mate will probably suit you better.
On the other hand, if you admire efficiency and speed, don't mind the odd bit of residual geekiness, and either don't care about appearance or are willing to customize heavily, Xfce will probably be more to your taste.
If you have definitely decided against GNOME 3 or Unity, then either Xfce or Mate will probably seem like an improvement. However, despite their similarities, the two desktop environments have enough differences that you should try both for several weeks before deciding between them.