The device that draws the most direct comparison to the PlayStation Camera is rival Microsoft's Xbox One Kinect, Xbox One's motion and voice control peripheral device (referred to by some as Kinect 2.0, since it is the next-generation version of the Xbox 360 Kinect).
The two most obvious differences are that the new Kinect comes standard with the Xbox One, whereas the PlayStation Camera is an optional accessory, and that the new Kinect is much larger and cannot be placed on top of your television. But there are some notable, less visible technical differences, too.
Both devices incorporate high definition cameras, but Xbox One Kinect has a single ultra-wide-angle 1080p resolution video camera, higher than the 1280 by 800 (roughly 720p) of the PlayStation Camera's dual cameras.
Xbox One Kinect does have another camera, hidden behind the faceplate of the device, but it is actually an active infrared (IR) camera. Among other things, it gives the Xbox One better vision in the dark and allows it to cancel out ambient light that could otherwise interfere. PlayStation Camera will be more finicky than Kinect about environmental lighting levels as a result. The new Kinect also includes an IR Blaster that throws out IR rays, allowing it to do things like control your TV or cable box. PS4 and its Camera do not include IR capabilities at all, so they can't be controlled by a universal remote, and certainly can't control your other entertainment devices, although there is talk of a BlueTooth remote for PS4 in the future.
Features of the new Kinect are currently more integrated into the Xbox One system than is the case with the PS Camera and the PS4. There are more possible voice commands for Xbox One than for PlayStation 4 as of early 2014, and you can make them without any menus on-screen. You can even turn your Xbox on and off with a voice command. It sits in wait for the "Xbox on" command when it is off.
Xbox One Kinect will pan and zoom to follow you while you are voice chatting on Skype, whereas PlayStation Camera requires that you stay in one spot to keep your face on screen during game live-streaming.
Both the PS Camera and the new Kinect allow for automatic login via facial recognition. You apparently have to confirm with the controller on PlayStation 4, though. Both also include multi-microphone arrays for accurate voice recognition.
If you already own one of these next-generation gaming consoles and want voice and motion control, you'll end up using the one that works with whichever of the two systems you have. But it's worth looking into all the differences if you're still shopping around for a new game system.