Tools > Options > Services > YouTube
That's how I have things set, and I don't think I've seen Media Center download 1080p off YouTube for quite some time now.
I just checked with a video that I know is 1080p, and Media Center grabbed a 720p version.
However, I only get 1080p when I view it in IE11 with Flash.
If I watch in Firefox via HTML5 (I don't have the Flash plugin installed - only what is built into IE11) then 720p is the highest resolution available.
If I use a bookmarklet in IE11 to download the video, I'm also only offered 720p.
YouTube is constantly making changes, and this has been happening for a couple of months now.
It seems that it mainly happens when videos have adverts on them.
If they have ads, you can only use HTML5 for playback when it's embedded on another site (720p) - it won't play on the YouTube site itself without Flash.
And for some reason if the video has ads, I have to switch to the HTTPS site in IE11 or else I won't get audio.
So while Media Center is not getting the full resolution version, I'm not sure that it's Media Center's fault.