The direct competitor is XFCE. There are a couple of advantages I personally find over XFCE:
- XFCE has a very severe lack of resources; in worst case, this translates to bugs (even severe) not being fixed for a very long time
- MATE has a very flexible interface (it's actually impressive how they have exactly the opposite philosophy as the GNOME guys)
I've been a longtime XFCE user, but when a couple of bugs started affecting my workflow, I had to leave it.
The worst case has a been a bug where around 25% of the times (if not more), moving files via file manager caused the file manager to crash. This has gone unfixed for a very long time (at least 6 months).
Despite what some people believes, it's not possible to swap the default file manager. While it's technically feasible, DEs have their FM harcoded in some places (ie. Desktop), which causes subtle breakages if the default FM is swapped.