My two cents. Sorry for the length of the post.
Disclaimer: A few monthes ago, I switched from MATE to GNOME 3. When Canonical announced that Unity was dropped and Ubuntu would use GNOME starting from v. 17.10, I gave it a try to see how the DE had progressed over the years (I already tried it years ago and it was pretty much unusable). After tweaking it with a few extensions, I now have a well working environement and I hesitate to go back to MATE because of some functionalities that I'd really miss (but I'd really like to go back to MATE, because while it's more polished, GNOME is also bloated and Mutter −the compositor− is a piece of crap).
1) Color management. It's something that is missing from a lot of Linux DEs. The "big ones" (GNOME, Unity, KDE) have it but the smaller DEs (MATE, XFCE, LXDE...) still miss what should be present in every modern DE IMO. GNOME has prefs to load ICC profiles for screens, printers and even scanners. I know there are some command line tools that can load a profile manually but having a software in the MATE prefs (especially if the settings daemon can monitor it) would be a welcome addition.
2) Better workspaces (virtual desktops) management. The dynamic workspaces of GNOME is a really interesting way of handling them. Basically, it has one when the session launches and opens a new one everytime there isn't one empty (i.e. you open a window, a new workspace is created; if you open something on it, another empty one is created. You always have a "spare" one).
In a related way, when using MATE, I had the workspaces applet pinned in the top right of my top panel: when needing to switch, I just moved the mouse "blindly" in the corner and moved the wheel to change workspace. It worked pretty well (except in Ubuntu MATE 17.04, where the applet is buggy) but I've found a different way of moving through workspaces in GNOME with an extension: moving the mouse wheel while on the right or left side of the screen to switch. It's a kind of hot corners functionality (except it's sides rather than corners) that works far better for me to quickly switch workspaces. I think something similar can be setup on MATE when using Compiz but not the other compositors (Marco / Compton). It would be great to have this implemented in MATE, though I'm not sure if it can be done independantly of the compositor.
3) Exposé mode. Kind of related to the workspaces management. GNOME has a true Exposé mode (by pressing a key, you get a display of all the opened windows and the list of workspaces), Unity has a somewhat similar feature with the workspaces grid. In both cases, you get a big preview of what is opened, allowing you to move applications between workspaces easily. I know there exists a DE-independant Exposé mode with Skippy-XD (though I'm not sure it's still in active developement) that can probably be used on MATE but I don't think it would allow to move windows from one workspace to another. I also know you can move windows in the workspace applet but it's too small to be really usable.
4) Mass renaming of files in Caja. I often handle a lot of files which I need to rename according to a pattern. Before GNOME, I used pyRenamer, a software made for mass renaming that works with regexps. While it works, it's not very convenient but a similar functionality (though more limited) is implemented directly in Nautilus: select a bunch of files, press F2 and you get a dialog offering the possibility to rename the selected files using a pattern (like append something before / after the original name, replace a string in every name...). It's really convenient.
5) Wacom tablets settings. This is quite specific and not needed by most people but when you have such a tablet, it's really handy to have a dedicated software in the prefs to set it up.