Sony confirmed with Polygon at San Diego Comic Con that PlayStation 3 wireless headsets will work with the PlayStation 4.
All PlayStation 4 consoles will ship with a wired headset, but if you already have a nice wireless headset for your PS3, at least you won't have to buy another just for your PS4.
Conversely, Microsoft is not shipping a headset with the Xbox One, and all Xbox 360 headsets are current incompatible with the next-gen model. Microsoft has said that it will work on an adapter for 360 headsets, but no word if these will be available at the console's launch.