I use the 55-200 for sports. My granddaughter plays indoor soccer which is known for low light and I have way too many of the photos that are difficult to get autofocus correct on. I am not going to use manual focus -action is too quick. I cannot use the f2.8 lens since the price is too high plus in soccer one moment the action is at the other end of the field and next is is close to you, so need at least the range of 55 -200.
When I am outside in sunshine I get great photos with the 55 - 200. But if the soccer game starts at 7:00 pm in the summer and ends at 8:30 pm, any photos after about 8 pm are mostly worthless - again the autofocus is too slow and the result ends up not sharp re focus.
In both cases I have already cranked up the ISO. My experience with the XT20 is that I am ok to ISO 3200, but ISO 6400 gets quite grainy. For the 55-200 I try to take the photos at at least 1/300 of a second. But the camera wants to drop lower than that since it max out the allowable ISO (3200), can't use a lower f-stop since it is already as low as allowed, and then results in taking photos less than 1/300.
I have already tried taking the soccer photos with the 18-55 at f/2.8 without zooming, but for too many situations the players are too far away, and even there at an indoor soccer game, if the players are close enough the auto focus is not fast enough even with ISO at 3200, fstop at f2.8.
Re the XT-20, other than the low light autofocus, I love the camera. I have the XT-20 and a Sony 6300. I now take almost all of my photos with the XT-20 - it is a much better camera to use then the Sony 6300.
If you want to see any photos, go to https://grandpajohnblog.wordpress.com. Almost all of the photo story photos were taken with the XT-20, with either the 18-55 f2.8-4 or the 55-200 f3.5-4.8. For closeups I have also used the Fujifilm extension tube primarily on the 18-55. Of course in my blog posts I don't include the photos that did not work in low light situations, and instead deleted them.