Difference between the Kinect and PrimeSensor?
PrimeSense is the company that developed Kinect hardware. The only difference is marketing and software. If you are wanting to develop a product for commercial use you will need to go through PrimeSense.

Edit:
For hobbyist work it will probably be easier to use a Kinect. There are already tons of people who have hacked it and there are now drivers public for the Kinect.