I had the X100V as precisely a walk-around camera - not the T but perhaps you may be interested in the experience. I now own a RX1R Mk1 which replaced it.
The ergonomics of the Fuji suited me best (I fitted a grip to both the X100 and the RX1R) - the hybrid viewfinder of the Fuji was useful and the battery life was better than the RX1R (for which I purchased new OEM batteries).
I bought the X100 new and after a couple of years of use, I was offered more than I had paid for it - still not sure why. For the period I owned it, though, it was in my coat pocket/work bag all of the time and I used it a lot. I found its resistance to dust useful).
The Fuji shutter is also ever so slightly louder and higher-pitched than the Sony, but that's a minor point.
I use the RX1R with an optical viewfinder; if you go down that route I suggest you give that a go; composition in bright sunlight is not so easy with the RX1R.
The Sony is hopelessly slow (AF and image writing); the battery life is not very good (I carry three at all times), the ergonomics are not brilliant. But the image quality.... 🙂