I have a Shield and the new Chromecast w/Google TV. Same versions of YouTube on both, but only the Shield version has the latest and greatest scrub bar and YouTube Music library features.
I recognize that Google TV is based on Android TV, and actually not technically Android TV anymore, but don't you find it odd that Google's brand new banner device has an older, less capable YouTube Music experience for all of these new converts who are buying into the Google TV ecosystem now?
Must be account specific I have the latest Youtube on both devices.