Microsoft's Xbox One headset will not be included with the Xbox One hardware.
The one-ear mono headset and microphone will be seen as an essential purchase for online multiplayer users, but will have to be purchased on top of the 429 console.
Microsoft has, however, pointed out that Kinect includes an integrated microphone, meaning that online voice communication will at least be possible.
Note that Xbox One headsets will include a proprietary connection, Ars Technica reports, meaning that standard headphones will not be usable without an adapter.
PS4 will include a mono earbud and microphone in the box. The current 250GB Xbox 360 does include a headset whereas the 4GB SKU does not.