Wii-mote camera works like a light gun and uses motion sensors for hand tracking.
Move uses the camera to track the hand which works like a 3D mouse (the most famous hand tracking device).
If you like to aim your controller like a gun in FPS then Wii-mote has the clear advantage.
If you aim by tracking your hand then Move has the advantage.
If you like waving your hands in the air like an idiot then clearly Natal is for you.