X100T it was. I tried a load of different settings but could never get it to focus on anything moving fast. The reason I sold it (for a sony A6000) was my 2 year old daughter was jumping on the bed, I took about 15 shots on medium continuous and all missed. I got a better shot with my phone. The x-t1 I never had a problem with, amazing camera as soon as you get used to the way the buttons all work.
All the cameras you have said have the same sensor and 2 will have the same lens. All three are very good. I would get a x100t over the x-pro1. The question is would you need the bigger x-t1 and the ability to change lenses over the x100t fixed lens. Do you want a centre evf? Do you want the bigger grip? An adapter for your OM lenses is also an option, the x-t1 has a dedicated focus button for helping focus.
I have gone through all of the above and have an x-e2 with 18-55 (amazing lens and I hate kit lenses as a rule) and a 35 1.4 as I like the 50mm fov. The x-e2 has the balance of price, size, interchangeable lenses, speed. I don't adapt any glass on it as the fuji lenses are great. I like the look of the 16mp sensor so not interested in upgrading.
What are you planning to shoot? The x-t1 and new 23mm is weather shield as well if you are sea fishing.