Here's why I like the YouTube app:
It allows you to watch a video and scroll through comments or suggested/related videos at the same time.
On all other apps and even the YouTube mobile site through Safari, you can't do this. I enjoy clicking on a video and while the video rolls, browse all the view comments and contribute my own. It's more engaging than watching a video, then stop video to go read comments, see a comment that says "this part was great" or "time stamp X:XX is really good!" and having to go reload the video to see it again.
No other app does this. That is what made, IMO, the original Apple YouTube app great. And now this Google YouTube app has retained this feature.
Much better than some "in the background playing" feature. To me, YT is about interataction, and this is a key feature.