I have successfully installed both Linux Mint 18.3 and then Ubuntu 18.04 on my Dell XPS 13 2in1 (Model 2728 with Intel® Core™ i7-7Y75 Processor) as a dual boot system with Windows 10. The process was fairly straightforward for both of these versions of Linux but I finally stuck with Ubuntu because of Gnomes better support for touch screens and the availability of a great new extension that links to my Android phone.
There are a few minor hurdles with the install process but these are not difficult as long as you are happy to boot into the BIOS (By pressing F12 repeatedly during the boot process with this laptop) and make a few adjustments. There is an excellent guide available on the Dell website here.
What works: Pretty much everything works well with both OS with these exception:
In Mint a right mouse click is activated by pressing on the right side of the trackpad or by using two finger tap but with Ubuntu you choose one option or the other but you can not have both.
The touch screen accepts touch to click and two finger scrolling with either distribution (But not in Firefox on Mint for some reason).
Automatic screen rotation works perfectly with Ubuntu / Gnome but has to be triggered manually in Mint and then both the trackpad and touchscreen inputs move the cursor in the opposite direction to what it should be. This renders it useless. If you want to use your touch screen enabled laptop in tablet or tent mode you are probably better off sticking with ubuntu.
Fingerprint scanner and face recognition do not work, but again there are plans to introduce fingerprint scanning in the next (18.10) Ubuntu release.
There is an issue with closing the lid when in sleep or hibernation mode in Mint. I have not been able to solve this yet but fortunately the system boots and shuts down so quickly that I have used shut down mode anyway. The same issue does not appear to affect Ubuntu.