The PlayStation 4 WILL support PlayStation 3 headsets.
Microsoft's redesigned controller for the Xbox One meant that current-gen wireless headsets were in danger of becoming obsolete. Any outrage or panic that would have ensued with the change has since been mitigated by Microsoft's plans on developing an adapter for Xbox headsets.
Sony has recently confirmed that PlayStation 4 will support PlayStation 3 wireless headsets and will ship with its own headset. Microsoft has confirmed that unlike the Xbox 360, the Xbox One will not ship with its own headset because it believes the new Kinect will be enough for voice chatting functions.
So gamers, rest easy that your PS3 headsets won't be useless paperweights with the new console generation.