I'd like to know the answer to this one as well. I suspect it's a difference in the composition of the two different types of water. Tap water has many added chemicals, but it also might remove some chemicals that are normally present in rain water. It seems that no matter how much I water my plants, everything in the garden perks up and looks better even after a short rainfall.
I see that Porkpal added a post before I was through typing this one. Yes, the nitrogen could be the answer.