I think the new dash looks great.
Hopefully they don't gimp the Kinect navigation. It is by far the fast way around as long as you remember the commands. With Kinect, you didn't have to go through layers of menus. In fact, you can directly go from one place to another which rarely happens in tech (you look at Windows, OS X, Android, iOS, any gaming console, etc., you have to drill down or up through menus). I'm hoping they make navigation more natural with the Cortana tech versus the Kinect tech (separate teams doing redundant work). With the current Kinect, you have to use the right phrasing to get it to do it. Cortana has more leeway with verbiage (though this freedom does lead to amusing experiences when Cortana totally botches what you were trying to say).
My biggest problem with the current One dashboard with the 360 dashboard is the ability to jump from party to party which is what a lot of us did in the 360 days. The One design almost traps you inside the party.
Another problem not addressed by the video is this: on the 360, you get a party invite during a game, you hit the guide button and then join the party. You had plenty of time to choose to join. On the One, if you don't accept the party invite the moment it's received, you have to go to the home page (out of the game), go to the notifications, and then join the party. and then switch from the snapped party app to the game or close the snapped party app. That whole process took way too long. And if you waited too long, the invite was already expired. The invite can expire on the 360 but I remember having much more time.
Even if you do hit the accept on the party invite right away, you still have to unsnap the app or switch snaps.