Headset (default and stereo) receives chat audio but won't transmit.

There is no stereo headset for the 360 that only connects to the controller.

The 360 controller only provides chat audio, there is no game audio transmitted through the 360 controller.

I'm referring to the Xbox One....probably should've mentioned that.

Unless a headset has multiple drivers that cover each piece of a 7.1 component system, a "surround sound headset" receives a matrix based simulated surround signal that is either a DTS, Dolby, or similar codec. The older simulated surround sound wireless
headsets transmitted the matrixes audio signal via a separate RF frequency via an external module after the module received the original audio signal from the console.

MSFT added a feature that will allow one to connect the modules from their older simulated surround head sets to the optical port on the Xbox one and still allow them to receive the intended matrix surround signal, but this will not have an affect on any
headset connected to the controller via the stereo connector.

The stereo connector will receive the audio signal from the console via a 2.1 stereo version, so it doesn't matter whether the game has its audio formatted for 2, 5, 7, or more components, the audio received will not exceed a stereo configuration.

That being said, there system will transmit the non-simulated surround signal via WiFi direct, so the non matrixes surround, stereo signal, should sound better than the matrixes surround signal of older headsets if the physical components of each headset
are similar. The problem is that there aren't conclusive specs aside from driver size have been listed about the current Xbox One headsets vs. the older headsets, so the limited reviews about the headsets are anecdotal at best.

In conclusion, until MSFT allows for the system to transmit a similuated surround signal and headsets that are capable of interoperating and recreating theta signal to a good degree are available, there will not be any "surround audio" transited directly
to the controller via the system itealf. All simulated surround signals will need to be transmitted via an externally connected RF module, but the new stereo signals should sound good if the hardware in these headsets are even the same as the old ones due
to the high mb/s rating of the Wifi Direct signal when compared to the older bluetooth or similar signals.

I hope this helps your decision process, and until a simulated surround signal can be transmitted from the console and a capable headset is provided, I don't see how the TurtleBeach or Polk headsets will have better audio than MSFT's stereo headset.

I hate to tell you this but the Xbox One console does not transmit game sounds or music through the Xbox One Chat Headset. If you're looking for an Xbox One headset that provides both game and chat audio, you should be
getting yourself an Xbox One Stereo Headset.

To set up an Xbox One Stereo headset, you can follow the steps provided through this link:

support.xbox.com/.../stereo-headset-set-up-troubleshoot

Same issue with iPhone headset. Audio works great, in party chat, others here high pitch whistle. While less than desirable, it may be that the adapter is not designed to work with inline mic's. Look at the last item in the list below. "Any 3.5mm stereo
headset (that uses the CTIA plug standard) can get stereo game audio by plugging into the adapter"

I hope that the headset can work.

From XBOX.COM Headset Adapter page:

For game audio:

- Legacy gaming headsets get game audio from the back of the console from the S/PDIF port or from your TV/receiver with RCA cables. Get chat audio by connecting the 2.5mm chat cable to the adapter

- New Xbox One headsets – get chat and stereo directly from the adapter. No need to connect anything to the console

- Any 3.5mm stereo headset (that uses the CTIA plug standard) can get stereo game audio by plugging into the adapter