Choppy audio and chat through wireless head set

Are you in the Xbox Insider Preview program? This seems to be an ongoing issue with preview OS builds, download the Xbox Insider Hub app and file a report. Also post about it here HTTPS://www.reddit.com/r/xboxinsiders

If not involved in preview, can I ask if consoles are connected wirelessly, and if so, does your router use 5ghz?

It may be that your Xbox one x is utilising a 5ghz Wi-Fi channel, and original Xbox isn't, and this use may interfere with the headphones. I had same issue at first with my turtle beach. It corrected itself when I switched off 5ghz channels on router, I
then switched to a wired connection.

If possible, hookup your offending console with a Ethernet cable to router, see if sound issue persists. If it does, then that's not the issue

i had the same problem. I strongly recommend following sandy the hippy post, as soon as i went onto a wired connection the problem was
gone

Okay so a 360 head set will connect to your xbox via optical cable for game audio (the more expensive wireless ones anyways) im not sure how the wired ones would work. There is a chat cable that will connect the head set to the controller for chat audio.

The xbox one versions that Microsoft and turtle beach have made will just plug in to your controller and you will get game and chat audio from that

I dont have that head set, but if you have a wireless connection to audio and have a wired connection to chat like I do with with my head set you have to turn off the game sound through the sound mixer from the menu and slide it all the way over to the
chat side turning off the game sound that comes through the controller. If you hit your menu button when you have your headset plugged in it should be part of the menu.