The Xbox Amazon video streaming app has always been pretty crappy. Significantly worse picture quality than streaming on a computer (unwatchable in my opinion), and odd/exceptional choices for navigation. Much of the blame for this is on Amazon, but some is on Microsoft as well for allowing Amazon to release such a poor quality application. I guess that is to your point on Apple vs. Microsoft: Apple wouldn't allow such a poor quality app on their platform, Microsoft gives them enough rope to hang themselves and doesn't stand in their way.
OTOH, I have an Xbox One and a 3rd Gen Apple TV and I much prefer the UI for video streaming on the Xbox to the Apple TV. Scrolling through things takes forever on the Apple device, while the Netflix and Hulu apps on the Xbox are a breeze and I can scroll through content with ease. Though, that's probably a function of the controller (much more input options on the Xbox controller than the Apple TV "remote").
