Together with a brand new interface and a new icon, both iOS and Android apps allow you to keep browsing their app with a small thumbnail of the video you are currently playing on the bottom of the screen.
Lets see if Google decides to also bring to Microsoft's mobile platform their new features, as Google itself blocked the last version of the YouTube app for Windows Phone. In David Howard words:
We think it’s clear that Google just doesn’t want Windows Phone users to have the same experience as Android and Apple users, and that their objections are nothing other than excuses. Nonetheless, we are committed to giving our users the experience they deserve, and are happy to work with Google to solve any legitimate concerns they may have. In the meantime, we once again request that Google stop blocking our YouTube app.