Besides the obvious vibration function for DS3, the other differences r:-

SIXAXIS - Lighter & cheaper. Use this for aggressive games like FIFA (if u r going to play 10 hours aday) that u think u r going to pull the analog stick out. U wont feel sad for it even the controller is out of shape since it is cheaper. This controller is also more suitable for those little 5-7 years old kid who comes to ur house n wanna play PS3 since they r going to tear ur controller apart. lol

DUAL SHOCK 3 - Heavier & more expensive. Use this for games like MGS4. Enjoy the force of vibration/rumble.