Did it ever cross your mind that maybe chatting to friends on an Xbox 360 whilst you are using an Xbox One might never be possible? Keep in mind that the original Xbox and Xbox 360 also didn’t share the features of Xbox LIVE before a “rant-off” is on your mind.
Major Nelson addressed the question via Reddit:
…based on what I know of the voice system, I would be surprised if this was possible. The Xbox One uses an all new wide bandwidth (read: better voice quality) CODEC, so I doubt they are compatible.
I originally thought that since Skype was powering all chat features for the new Xbox One and that the current Xbox 360 does not hook into that system might possibly be a reason. However the issue is CODEC’s. If you’re friends are not buying Xbox One’s for “whatever” reasons, best start saying your farewells come November.