I finally got around to trying out the media server stuff on Xbox One and it actually works decently. It's just barebones as hell.
As a comparison, the Xbox 360 made every video its own folder so that you could only watch one video at a time and have to constantly navigate this terrible system of folders to watch videos on your server. On Xbox One, it is shows the file structure as it is on my PC and lets you watch them consecutively, which is also how it's done on PS3. It's so much better in just that basic way than it was on Xbox 360, but it still pales in comparison to PS3.
The things I don't like about it is that the videos are listed like everything else, as tiles in columns that are two tiles high to make it harder to scroll through a long list than it should be if it were just a list of video titles, and there are no options for the videos themselves. When I play a video, I can only pause, fast forward, and rewind. I guess there is also the ability to skip to the next/previous video without backing out to the directory, but that is only possible by tapping left/right on the d-pad or moving the left stick left or right and that's really dumb. Microsoft has always been bad about mapping video/typing controls to a controller, so I'm not surprised. I'd like volume controls on videos if they're naturally louder or quieter than I'd like them to be and some better ways to jump around in a longer video, as just offering fast forward/rewind is not enough. It also needs the ability to resume a video from where you left off if you back out to the directory along with a way to browse my list of videos while the current video plays so I can find something else to watch when I don't want to watch consecutively. It would also be nice if I could download videos locally to the Xbox One from my network if there was something I particularly wanted to watch in that manner, though I don't know if Xbox One has a local video storage option yet or if it still only supports external videos. There's no way I'd move to Xbox One from PS3 for this stuff until all of that is addressed, which I have my doubts that they'll do all of that.