I have an XPS 13 and run Linux on it. The drivers for the touchpad were very rough with the version of Ubuntu it shipped with, but updating to a Kernel version > 4 fixed all my problems.
1) the touchpad never worked; 2) the keyboard still has problems; 3) some of the more important programs look just horrible on Linux, as the resolution is just too high; 4) sometimes WiFi just does not work;
...so much for the Sputnik project.
Also, regarding #3, I've heard Linux Mint as great HiDPI support in their last version.
The current situation with XPS 15 seems much worse: http://ubuntuforums.org/showthread.php?t=2301071
For decent experience, one should wait until April until 16.04 comes out. And some issues will probably remain for a release or two after that.
Overall the only problems I face is with - GTK2 apps, they look awkward. Eg. very small icons - Spotify, Steam, Skype will look very small
However the biggest turnoff is that whenever I connect to external display (1080p), I have to apply a weird command with scaling and panning options. This results in blurred look, a bit lag and fan spinning hard. I wish there was some option to do selective font scaling based the screen.
Also take out the broadcom wifi and burn it with fire! Replaced with Intel wifi card and have zero wifi issues.