Debating is fun as long as there is good logic and less emotion. This is why debating with my wife is not fun. Most of the time she is the one with the logic and I have the emotion so I pretty much lose all the time...no fun.
I like both Sony and Fuji mirrorless cameras but I have just decided to stick with Fuji for now and hopefully my post will provide some insight that will be helpful for you in your decision making process.
Here is a list of camera equipment that I have purchased with my own money as the basis for my decision:
Sony a6000, Sony a7r, Sony a7ii, Zeiss Loxia 2/35, Zeiss Loxia 2/50, Zeiss Batis 1.8/85, Sony 70-200mm F4 G OSS
Fujifilm X-T1, Fujifilm X-Pro2, Fujinon XF 2/35, Fujinon XF 1.4/16
You can see from my portfolio the type of work that I do but for the most part these mirrorless cameras are used on the personal side for family, street, travel, etc. This is not to say that they could not be used professionally because the quality is there for the most part and there are plenty of people who seem to be ok with delivering these files to clients.
I'll try to boil down my conclusion to the main points which differentiate the Fuji from the Sony. If I do not mention something you feel is important then that probably means I feel each system offers similar benefits.
You probably think I will talk about the amazing quality of the Fuji JPEGS (which are amazing) but this is not what I mean. There are times when the RAW files from the Sony seemed mushy without much depth/character. I know this isn't a technical term and I don't know how else to describe it. This didn't always happen but it did happen from time to time for no apparent reason.
This has yet to occur on the Fuji.
There were 2 things that annoyed me about the body of the Sony a7r and a7ii. The first is the SD door which opened up on a regular occasion by just normal handling. The second is the ISO button on the back which continued to be pressed by normal handling causing the ISO to change while I was handling the camera leading to shots being taken with improper exposure.
The Fuji body does not have these issues. On top of that we all know that Fuji makes some sexy bodies.
3. Wifi Transfer
The transfer function works fine on both Sony and Fuji but the Sony always transfers files that are too small. I care about the quality of images I put on Instagram (@tom.f.watson) and Facebook but when I posted images directly from the camera using Sony the files would always be smaller than 1080px across which isn't even optimized for Instagram. They look even worse on Facebook.
The Fuji files transferred to my phone are at least 1776px which work great for both Instagram and are good enough for Facebook.
4. Battery Life
When I shot with the Sony I felt that I always had to leave the house with a fully charged battery and if it was going to be an extended day of shooting that an extra battery could be required. I would also turn off the EVF at the eye piece and only use the back monitor to conserve on the battery life.
The Fuji is able to manage power much better. I have not had to leave my house with an extra battery and most of the time do not go out shooting with a fully charged battery.
Thank you for sticking with me to the end. I'd love to hear your thoughts if you have experience on both systems.