I guess my perspective is that generally most of the cameras on the market right now are pretty good. Fuji has an excellent jpeg engine, but otherwise the output their cameras is pretty similar to the output from other cameras on the market. They have the whole X Trans sensor thing, but truthfully, that doesn't seem to be here or there, except it makes it so that DXO Mark doesn't test their cameras.
The most important thing is whether you like the handling of the camera. If you like the Fuji better than you should go with it. You are going to enjoy your photo shoots more if you connect better with it.
As far as the output of both cameras goes, I really think you should be able to tweak them so they give similar results. I shoot RAW mostly, but when I shoot jpegs, I get very similar results. What makes a portrait work is generally a combination of lighting and composition -- not so much the details of editing. People do often like a warm tone to images and it's pretty easy to do that in Lightroom or whatever post processor you use.
As far as the K-1 specifically goes, I really like the dynamic range, the ability to shoot high iso. Backlit shots can be tough, even with APS-C size sensors as it is easy to end up with a bunch of noise in your subject and the K-1 can bring up shadows easily without a whole lot of issue. As I said before, you need to shoot with what works for you and crowd sourcing your decision won't really change that.
(two shots with the DFA 24-70mm on K-1)