They are an integration of the game audio channel AND the voice channel; if you get the right set. If you dont your are stuck to the voice output mixed with the game audio which makes chat very difficult. Basically you want an Xbox specific product that plugs into the controller.
The X1's for example connect to a USB power, ie back of the XBOX, then you can eaither plug the audio plug direct to the headphone socket or use into the red and white RCA cable to 3.5mm jack adaptor that allows in my case the VGA cable to connect from the Xbox to both the headset and the TV. Then there is a puck thats about 1 foot on the wire from the headset, the controller plugs into that unit and its where you control audio volume and mute, with the controller puck having the voice channel volume. Say voice options to 'both' and you can hear your own party and the other players in game chat. For example being dead on S&D on COD when you are in a party is rather useful
X1's are nice, dunno if X3's would annoy me with the battery issue. Although I think they may have slightly better sound and you can hear you own voice back through the set which is probably pretty useful for regulating your own volume. Wireless on them is IR rather than Radio AFAIK aswell.