Updated 30-Jan-2022
Summary -- The superiority of XFCE or Cinnamon comes down to use cases, and of course preference -- de gustibus non est disputandum.
XFCE Superiority
XFCE is a delight in many ways, when compared with Cinnamon:
- Less memory and processor utilization
- A bit more stable (though this could be an instability with Nemo)
- Faster/easier to configure (the settings menus are much better organized with fewer top-level items)
Cinnamon Superiority
At the same time, Cinnamon has definitely fixed/improved a few things:
- Keyboard settings to reconfigure standard keyboard remapping (Win/Cmd/Super remapping, CapsLock behavior). See this Superuser QA for hints as to deal with this issue.
- Shortcuts on the start menu, ease of adding apps from the menu to the dock, and in general a more elegant start menu w/ search, better spacing
Beyond these issues, everything else seems to be about applications. Both can do everything else more or less similarly.
- Note: one can install Cinnamon on Debian directly, or try Linux Mint Debian Edition (LMDE), or simply standard Mint (an Ubuntu derrivative) and Cinnamon. Cinnamon is also available for a few other Linux distributions.
Nautilus (completes) Nemo
Nemo is simply unstable. Try doing some drag-and-drop and it soon slows, hangs, quits. Thunar is nice, but there is no handy search or buttons to toggle between views. Everything has to be committed to remembered keyboard shortcuts. Silly. Rename is generally always grayed out (without any explanation).
Nautilus is not perfect by any means. A seeming limitation of the icon view size set to max 133% is a disappointment. However, beyond that it is very good and definitely an improvement over Nemo for some things (rename and cut/copy/paste) while Nemo generally is better for browse and search.
The bottom line is that while Cinnamon has greater resource demands, and a bit less stability, it has a better dock/menu interface and better keyboard configuration support. This makes it a premium modern desktop for Debian and Ubuntu (via the Linux Mint Debian Edition (LMDE).
XFCE - Better Resource Management for Low End Devices
Either Debian + XFCE or the Linux Mint XFCE edition are appropriate for low-end devices, say those with 4gb or less of RAM. This would be appropriate for the Asus C101PA Convertible Chromebook.