My only real experience with Backwards Compatibility so far is when we played Gears 2 Horde Mode. That felt good for the most part. The only thing I remember feeling a little weird was that we couldn't invite each other to the game from the Xbox Ones friends list or from the Xbox One party chat we were in.
This doesn't seem like a big deal until you find out that the Xbox One and Xbox 360 friends lists are totally separate. Even though were were friends on Xbox One we weren't on Xbox 360. I also had a friend invite sitting in my 360 message list that was several months old that I had never seen before. The person sent me the request from their 360 but it only shows when I am in backwards compatibility mode and looking at the 360's guide.