Fuji UK were kind enough to lend me an X-E3 to test out for 2 weeks. I'd asked them to send me one as the idea of a smaller camera that's a bit lighter seems quite appealing these days.
My test ground was Le Mans Classic as a camera to carry around when I wasn't carrying around my more serious Sony Gear (A9 with heavy lenses). Right off the bat I noticed how light this setup was going to be. The Fuji with a 35mm ish lens on it was about half the weight of similar on the A9.
i haven't used a Fuji camera for some time and the menu system was a bit complicated at the start but after some playing around I managed to get the camera set up how I wanted and learnt that most things you need to change can be changed via the Quick (Q) menu.
Once I'd set up the camera it was extremely easy to just get on with shooting. I don't often shoot with the screen on the back of the camera but with something so light I used this functionality quite a bit using the touch screen to set the focus point before composing the shot. The viewfinder was decent as such that I never noticed it getting in the way of me taking photos. I'm very used to mirrorless systems now and a digital viewfinder just makes getting the right exposure so easy. Having an exposure compensation dial on the top of the camera makes adjustments nice and quick. The dials for aperture on the lens and shutter speed on the top of the camera are a really nice feature and definitely help make the shooting experience feel more analog. I find some small digital cameras make you use the menu system all the time and it really slows you down.
Autofocus: The camera was very responsive and in single shot mode I didn't have any problems. In continuous focus mode it was a bit slower to react but was good enough to enable me to capture most of the shots I needed. I wouldn't go for this camera if you NEED fast continuous autofocus under challenging conditions (but then again you would need to be looking at much more expensive cameras and systems).
Conclusion: For the price (£799 last time I checked) I think you get an amazing small camera that would be a perfect carry around. Couple it with a light fuji prime and for around £1k you have something capable of delivering amazing results. I'm really very tempted to pick one up myself (my only reservation is I have a lot of Sony glass so something from the same family might make more sense). I shot with the 23/35/50mm F2 fuji lenses which were so light it's crazy. I'd love to try out the f1.4 versions as I believe they are also quite small.