I would propose that the Fuji wins on overall IQ and high ISO performance, with an overall greater richness and depth in the files [though the Olympus offers excellent image acuity and strong performance, too, below ISO 800. I prefer not to go past 1600 with the Olympus [3200 if I must], though with the Fuji I will push to 6400 if need be. 3200 most assuredly looks better from the Fuji than it does from the Olympus.
Generally, however, I find that the Olympus sensor needs a better "quality" of light to perform optimally.
As Kevin said, Capture One is excellent for the Fuji files. Meanwhile, the Olympus files seem to do best with DXO Optics Pro. Olympus Viewer software is excellent, too, but it's dog slow and the interface isn't particularly intuitive.
Ergonomically, it mostly comes down to personal taste when comparing the X-T1 and E-M1. The former is more retro, something we veteran shooters often tend to gravitate to, and a facility that enables fast control of dials without having to hunt through menus, potentially speeding up operation.
The Olympus body is probably a bit more rugged overall, and the deeper grip is definitely beneficial. Despite a more contemporary control interface, the Olympus controls are superbly laid out once you have everything configured to your taste. Olympus' menu system is atrocious, though.
I would say EVFs are a wash. And I would say lens quality between the two lines is similarly a toss-up; both make superb optics with lots of choices for discerning shooters.
Autofocus speed goes to the Olympus … by a nose. Though the X-T1's new tracking modes with the 4.0 firmware update offer more versatility, I think.
The m4/3 system will be a bit smaller overall once you factor in lenses.
At the end of the day, you have to ask yourself: what am I going to shoot with this camera?
There will definitely be an X-Pro 2 next year, and you can expect at least 24mp. That's all I can say.