Nice, so Unity is finally an option for me. Now it would be nice if the Unreal editor had official Linux support as well. (I know there's Wine, but it didn't work too well for me.)
Both are general purpose engines and can be put towards a wide variety of game genres. Out of the box, UE4's editor comes with about half a dozen templates (FPS, top-down, side-scrolling platformer etc) for rudimentary intro projects.
Unreal Engine is somewhat harder to use, but it's graphics engine is a bit closer to the cutting edge - it's the go-to engine for AAA devs these days. Unity's main user base (for people who use it to make games - some use it for academic ends, or for tech demos) tends to be the indie game scene.
They do the same job, but differ in the technical aspects and ease-of-use, and business model (though both are aiming to lower the barriers to making games), and they tend to cater to different segments of the market.
I have been running UE4 on linux since the community builds around 4.6, but 4.8 official builds are now pretty fully functional, minus the launcher, and my main gripe: having to build linux dedicated servers on windows...
I am pretty dedicated to releasing for SteamOS as a main target platform, and have been trying to untether from windows. I have a few friends are love unity and want me to join projects but my main complaint has always been that there was no linux editor. Looks like I will have to test out the this unity test build.
https://wiki.unrealengine.com/Building_On_Linux