You might just find that this pocketable Fuji is way superior to your 5D MK3 in most respects except fast tracking AF
I know I prefer my Fuji X cameras (X-Pro1 and XE-1) to my 5D MK3 with any L or Zeiss lens you care to nominate.
I've owned or tried most of them and they are soft and lackluster in comparison...
Fuji cameras are pretty - I have an X10 because it has decent image quality, is reasonably small, has a manual zoom, and looks cool. Some of my friends have bought X10s too - simply because it looks stylish (they're not interested in taking photos with it - they have iPhones for that). I've tried getting to the point where I can go out on a serious photo mission with nothing but my Fuji, but I always find myself wishing I had my 5D3 or 1V with me. I'm just an SLR person really. I like the responsiveness and the no-nonsense layout of the controls (especially on the 1V). I've handled the XE-1 at my local camera shop and felt that it was still quite a large camera and I couldn't really see the point in buying one when I already have SLRs. The XE-1 is well known for its sharpness though - it lacks an AA filter which contributes to this. (I'm not sure how this affects its moiré aliasing though - probably badly).
Today I had a play with an EOS 6D with the new Sigma 35mm f/1.4 lens attached. The lens was gorgeous. The 6D just felt like a x00 series EOS, but full-frame... Sturdy and trustworthy, no doubt, but overpriced for what it is.