The NP-W126S is identical to the NP-W126 you use in your X-E2. The only differences are that the S battery handles the heat that using 4K video causes better than the regular NP-W126 does and costs almost twice as much. Otherwise performance is identical and unless you are shooting a lot of 4k video, you can use your regular NP-W126 in the X100F. Fuji came out with the NP-W126S when the X-T2 was released.
The good news is that you will only need to carry one type of battery and charger for both cameras. Like you, I have an X-E2 and I also have an X100T, which uses the NP-95 battery. So, if I go anywhere and take both cameras, I need to have two different sets of batteries and chargers.