I'm using the official Microsoft Dongle for the original Xbox One controller, a wired 360 controller and a bluetooth Dualshock 4 using DS4Windows as an X-input wrapper. I experience lag with either of these controller methods. And for every one of them, the input latency seems to spike much higher at random intervals. There are times when I'm scrolling through a game list, and BB will completely become unresponsive for 2-3 seconds. That's usually the worst case. But many other times control input will drop out for 1-2 seconds, or even a sub second.
I have not tried bluetooth with the Xbox One S controller because all of my other input methods are using x-input in some fashion, so I don't think it is isolated to the physical input method. Also, I'm running Win10 on an MSI motherboard.