I have the V1. It is way faster than my old P1 at focusing. Probably the thing that has impressed me most about this camera over my old one is the operating speed (focusing, browsing pictures, etc.) and the quality of pictures in low light.
How fast it is for focusing depends on lighting. But, I would say in bright conditions it is near instantaneous (less than half a second). About 1 second indoors in reasonable light. And in dim light about 2 seconds. In dim light it uses holographic auto focus so you get real good flash light pictures.