Linux gives you a huge choice of user interfaces, Xfce, Cinnamon, Gnome, and many others. Which one is the fastest?
Start with your computer. Does your computer have a GPU, a Graphical Processing Unit? Some user interfaces can use a GPU for speed then switch to slower CPU processing on computers without a GPU.
The GPU might be a built in chip or an add-on card. There is a huge difference between the slowest and fastest GPU. The Cinnamon GUI will be faster with most GPUs.
When the GUI accesses the GPU, the connection is through specialised software provided by Linux, something that is called a driver in Windows. Linux may fail to provide a good interface for some GPUs, leaving your GUI struggling. If you have any applications failing to work fast with your GPU, your GUI will probably suffer the same problem.
The GPU processing is usually for special effects and a good GUI will let you switch off those special effects. The MATE GUI is supposed to be faster than the Cinnamon GUI but when I tested Cinnamon with all special effects switched off, Cinnamon ran as fast as MATE.
Speed comparisons are only valid when they have the same sort of GPU as your computer.
CPU clock speed
Your computer processor, the CPU, can have a clock speed from less than 1 GHz up to 5 GHz. The clock speed makes a huge difference.
At the 1 GHz end, the CPU is slower than everything else, other than a magnetic disk. You need a light weight GUI like Xfce or LXDE. Replacing the magnetic disk with any SSD, the cheapest SSD, will make your boot times and application start up jump in speed far more than what you get by switching to a different GUI.
At the 5 GHz end of the CPU speed range, you will not notice any difference between the different brands of GUI or from the use of a GPU. SSDs will make a difference and you should invest in a faster premium SSD to keep up with the faster CPU.
Many modern computer processors get their overall speed from using many cores but may run each core at a slow speed to keep down the power usage and heat generated. Some applications can use many cores for fast throughput. The average GUI rarely uses more than one core.
A 16 core processor might make some applications fast but not your GUI. An 8 core processor running at 5 GHz will be faster than a 16 core CPU running at 2.6 GHz.
Xfce is often the fastest GUI for boot speed, mainly due to Xfce not reading a stack of configuration details. The more flexible GUIs have to store all this settings somewhere and some of them store the settings as a mass of little files.
Replacing a magnetic disk with an SSD will improve the boot time more than any difference in speed between the various GUIs. If the boot time is still too long after you move to an SSD, look at Xfce.
With Xfce, you will lose configuration flexibility compared to a GUI like Cinnamon. You might find you can keep the flexibility of Cinnamon, or you current GUI, and improve boot time by removing things from the automated startup process.
As an example, I let some web development software default to starting automatically at boot. I then removed the packages from the automatic startup to gain a few seconds. On most days, I do not use the tools which means most boots wasted time starting something I would not use.
Application startup speed
Applications are slow to start when they load a mass of components and files. SSDs will increase the application load speed by far more than a change of GUI. I would focus on how easy it is to start the application when using a specific GUI. I choose Cinnamon for the nice menu system.
Cinnamon also makes it easy to add new programs to the menu. The last time I used Xfce and LXDE, changing the menu was painful.
Memory usage is the most talked about difference between GUIs because it is the easiest thing to see and it is critical on small old machines with a main memory as small as 1 GB. The Raspberry Pi computer started with 0.25 GB and uses LXDE for the user interface.
Xfce uses more memory than LXDE. Your choice of application makes a bigger difference than the differences between Xfce and LXDE. Replacing the Chrome Web browser with anything else will make ten times more difference.
LXDE internal uses something called Openbox. You can use Openbox without LXDE to reduce memory usage further. Most people find Openbox unusable without adding extra software and they end up with something like LXDE.
The Raspberry Pi developers made LXDE really small by minimising everything in LXDE. If you want the smallest Linux + LXDE commination, look at the raspberry Pi Desktop distribution of Linux.
Xfce is a small step up from LXDE and appears to be not much easier when you have to configure something. MATE is the next step up, is about the same size as a trimmed down Cinnamon, and did not offer any advantage over Cinnamon in any of my tests.
Cinnamon is bigger than MATE but not by much in recent releases. I run Cinnamon with special effects switched off, giving me an easier configuration, compared to all the other choices, with very little overhead increase compared to MATE.
KDE is the big GUI that few people use on laptop or notebook computers. KDE appears to be limited to desktops with significant hardware.
Gnome Shell is another GUI somewhere in the middle with about the same usage as Cinnamon but not as nice a user interface. Budgie is a new GUI that some people say is lightweight but measurements show Budgie to be worse than the more popular choices.
Many new Linux users are escaping from Windows. Cinnamon is the easiest switch from Windows 7. Xfce looks and works more like Windows XP. Nothing is as bad as the user interface on Windows 10.
There are GUIs designed to look at work like MacOS. I have had some unfortunate experiences where customers provided Apple Max computers instead of something useful. What a waste of time. When you replace MacOS on an Apple computer, you are probably like me, looking for a GUI that saves you time instead of forcing you to work slow.
Choose a good Linux distribution
You could pick any distribution of Linux then replace any supplied GUI with a different GUI. The process is painful and unreliable. Choose a Linux distribution with the GUI you want.
Look for a reliable Linux distribution with good user support in the distribution's forums. The major Linux distributions are available preconfigured with the most popular GUIs. Ubuntu had an LXDE edition called Lubuntu plus several other editions.
The very popular Linux Mint has editions with Cinnamon, MATE, Xfce, and LXDE. In their case, the Cinnamon, MATE, and Xfce editions have long term support releases. The LXDE edition has a different type of support, a Debian based rolling support I might recommend for experienced developers but not for first time Linux users.
Cinnamon is the first choice for people escaping recent versions of Windows and for use on any computer with enough power to do serious work. The only configuration required is to switch off some effects.
Xfce is the next choice, for Windows XP era computers, for five year old cheap computers that were under powered back then, and for older computers with minimum RAM that cannot be expanded.
The Raspberry Pi Desktop edition, using LXDE, is the next step down in resource usage and a good choice for education. The Raspberry Pi Raspbian edition is the first choice for the tiny Raspberry Pi credit card size computers. There is really nothing useful that is smaller than a Raspberry Pi.
Replacing a magnetic disk with an SSD gives you far more benefit than changing your GUI.
Visit the product support forums before selecting a distribution or GUI.