I have cross-compiled from Windows to Linux using UE on Windows. Although I love Linux and I enjoy working on it, I would never consider moving my development over to Linux in its entirety.
From my experience the whole UE4 pipeline is geared towards Windows and/or Mac and using Linux full time would be a pain. Some of the processes that are painless and easy on Windows would require a lot more effort on Linux.
If I were you, develop on Windows and cross compile to Linux … it works perfectly and had proven less strenuous and painful then when I first tried to do it on Linux.