Device Support
Kinect is made for, and supports, the Xbox 360 console, part of the "current generation" as of July 2013. The equipment can also be used with Windows computers as Microsoft has released the necessary drivers and code for developers. EyeToy, on the other hand, was designed for the PlayStation 2, though it also works with the current-generation PlayStation 3. It's successor, the Eye, is specifically designed for the PS3. Neither the EyeToy nor the Eye have specific support for PC use; however, you can download third-party drivers to make either device act as a webcam and microphone.
Equipment
The Kinect is a single device with two cameras -- one for image capture, one for depth perception -- and four microphones for filtering out background noise. The EyeToy and Eye are both single cameras with a built-in microphone that can be affected by background noise and cannot distinguish voices. While the EyeToy and Eye are the same size and shape as most PC webcams, the Kinect is a much wider rectangular shape, and has motors to automatically tilt it up or down to get the best focus on the player.
Controllers
The Kinect does not require players to use any form of controller and can instead take instructions solely from a player's movement. The Eye does not capture input commands, but instead uses the video of the player to create an on-screen image mixing real and game footage. The EyeToy can accept commands through two optional handheld controllers that emit a colored glow and track the player's hand movements.
Depth Perception
The use of two cameras means the Kinect can detect how near to or far from the screen the player is standing, and thus track movement in three dimensions. The Eye and EyeToy only track in two dimensions -- up and down, left and right. This restricts the options open to game designers for tracking movements and narrows the range of possible input commands.
Non-Gaming Uses
The Xbox console includes support for Kinect controls outside of gaming. For example, you can swipe a hand to move through a menu, or use voice commands to make a selection. The PC support allows for a wide range of uses of the technology. The Eye and EyeToy are limited to support for specific games, so you cannot use them for menu controls or other console applications.