I've been shooting X-Trans cameras for a couple years now and second what most folks and reviewers perceive - there's a certain 'Fuji look' and it's not only about the colors or the glass.
I don't care too much for SOOC jpgs, no matter what brand, have tried most of the available RAW converters for X-Trans (and X-Rite to generate my own profiles) but whatever I tried the results still look different from what I get from my Sonys or ex-Canons, especially at 100% or higher magnifications (I'm not much of a pixel-peeper though).
Heck, at the end of the day it all boils down to personal preferences and compromises - there's no 'perfect' camera/system. I'll continue to use (and enjoy) my X-Trans bricks for personal documentary stuff and won't sell my remaining Fuji gear anytime soon, but will use my Sonys with legacy glass for some long-term projects that involve huge prints.