Kinect vs Move
Both systems released as 'responses' to the hugely successful Nintendo Wii (although Sony's Move did exist before the Wii was released), Microsoft and Sony launched two competing controllers for their current PS3 and Xbox 360 consoles. While appearing very different in the way that they are used, they are not that different in the way that they work.
[edit] Hardware
Kinect
Kinect is basically two cameras, but there is a lot more to it than that. Inside the stand is a small electric motor and a gearing system. That allows the camera to turn so you can't walk out of it's field of view. Looking inside the case, which Microsoft have made very difficult to open, there are three small motherboards stacked on top of each other. They handle the processing because the 360's processor is already at full power running the game. On the third motherboard there is a webcam that is almost identical to the Playstation Eye's. There is also an infra-red camera with a 320x240 resolution and an IR projector that allows the infra-red camera to detect depth. Only the IR camera is used for motion tracking, but, unlike similar systems like the EyeToy and newer Playstation Eye, the camera can see in 3D (not the normal camera but the IR camera). The system requires an external power supply unless used with the 'Kinect' port on the updated Xbox 360 S. It kinects (lol) to older 360s using a USB port.
Move
While similar in appearance, Move works in a completely different way than the Wii - and it's much more accurate and does not lag. The system uses the Playstation Eye camera which connects to the PS3 using a USB port. The controller uses Bluetooth to communicate with the PS3 and contains a 32-bit ARM processor which receives communications and performs tasks such as changing the colour of the LED light. There is a rechargeable battery, a force-feedback motor, a magnetoscope, an accelerometer and a gyroscope. They are all fixed to a motherboard slightly larger than one of three Kinect boards. However, most of these systems are 'backup' as the LED light is what tells the PS3 the location of the controller. The controller charges via a standard USB cable but also has an 'EXT' port which presumably will be used for some future product, but only Sony know what that is. The LED light supports 246-bit colour and is actually quite bright.
[edit] Accuracy
We have a clear winner for this category. If you read about the Kinect and presumed it would be able to fully track a human body with accuracy and no lag then... think about things a little more in the future. The system has nothing to actually track except the shape of a person - and that's a difficult task. There have been reports of up to 1 second of lag and inaccuracy is clear (shown up more by the fact that Microsoft did not actually show the system at their unveiling - the on-screen images were pre-recorded). On the other hand, Move is accurate to 1mm in two dimensions and 1cm in the z-axis. I have Move and I can confirm that accuracy, in fact, it is more like 2mm in the z-axis.
[edit] GAMES AND GAMEPLAY
Yes, it deserves to be in capitals because it's the most important thing.