The UE4 editor can be built for Linux, though they don't have official stable builds yet.
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.