Main reasons would be increased portability, lighter glass for hiking, possibly increased weather sealing vs the 6D, and 4K video, in that order.If your main reason for switching is 4K video, I'd look at an A7RII, with a Sigma MC-11 adapter. You get 4K video, you don't have to give up the full-frame sensor, you can keep using all your L glass (the MC-11 works pretty well with Canon lenses), and Sony's native glass is getting better and better (not necessarily cheaper and cheaper, but comparable in price to Canon L lenses anyway).
You're likely to find some good deals on it in the next couple of months if you want to buy new, otherwise there will be lots of folks selling them second hand, like Zefah in this very thread.
I'm aware of the caveats of moving from full frame to mirrorless, as I did that before, going from 5D classic to Oly m4/3. Where Fuji interests me are the 50-140mm and 10-24mm. The 50-140mm in particular is one of the first mirrorless lenses that I've seen consistent DSLR-caliber quality from. I don't think I have interest in retaining my Canon glass if I move to a new ecosystem.
I found Oly lacking in a few key areas...most notably their focus tracking in continuous focus modes. It simply can't keep up with a kid running around or a moving subject. The X-T2 reviews I've seen all laud the AF and continuous AF, which I'm sure would be a net gain over the 6D which is more suited to landscapes.