What are the advantages of PS3 Move

You can read more here but the gist is

1. Don't have any light sources directly opposite the camera. Light sources that flicker, or other TV etc. will affect performance.
2. You should be sufficiently far away from the camera. They recommend 5-9 feet, in my experience 6 feet is good.
3. Stuff should not be obstructing the camera and the camera should be pointed to the top half of your body. You should stand and play the game, if you sit and play, the system thinks you are a weird human body and does crazy stuff.
4. Contrast with the background. if you the color of the move controller blends in with the background, you will have problems.

There will be fewer games that support Move at the moment because it's a relatively new device. If you look today you might not find the games you want on the PS3, but as time passes more games will be released that make use of Move.

Digital Trends has an article that compares the Move to a Wiimote. The basic difference is:

While the accelerometers inside the controller act much as a Wii does, the balls provide what Sony calls a zero point – an absolute location in physical space for the system to peg all the other data to.

While the Wiimote uses its camera to locate the IR emitters in the sensor bar placed above or below the screen, the PS3 uses a camera to locate the glowing ball on the Move. I've never used the Move so I can't tell you whether it's better or worse than the Wii.