One of the things I really don't enjoy about Microsoft's is the proprietary nature they take when it comes with peripherals. You can use pretty much any Bluetooth or USB headset with the PlayStation 4 as well as most any wired one to connect to the controller for sound and voice. Not so with the Xbox One.
There's no official adapter out right now to let you use a wired headset plugged into the controller, but you can make one pretty easily. You'll just have to cannibalize the included headset to do so. Instructables has some nice instructions on how to do it and all you need is a 2.5mm adapter that will run you a few bucks and a soldering iron.
You take the included Xbox One headset apart, solder the wires onto the adapter, and off you go. It looks pretty simple and you'll be able to use any wired headset you want with your Xbox One. Pretty cool if I say so myself and it won't cost you an arm a leg and will most definitely be less expensive than what Microsoft puts out.