Over the years I have installed many systems and run many water tests of rainwater systems.  For one client, I tested the neighbors well water (sharing the well was an option) and her harvested rainwater.  With the exception of the presence of bacteria which is in all rainwater and surface water and easily treatable, the catchment water had significantly lower mineral content and lower pH. 

Many systems are installed purely for irrigation purposes and I am convinced this water is much healthier for our plants than typical municipal water.  I have seen no direct studies on this, although logic tells you that water containing chlorine (the most commonly used disinfection in public water systems) is not great for the soil over long periods of time.

A couple in Ruidoso, New Mexico took it one step further and came to the conclusion that the local city water was not healthy for them and with the assistance of relatives, friends, and local professionals installed a rainwater catchment system to get purer water. 

Per this article:

When Judy, a retired registered nurse, began experiencing some health issues, and Tom wasn't far behind, the couple tried to pinpoint possible causes and decided that while the village of Ruidoso's water was deemed "safe" to drink, that some of the chemicals used to arrive at that point might be contributing to their symptoms.

"We've had the water tested and it has passed with flying colors. People could do this simpler by using the village water and coming up with a lot better water by bringing it in and filtering it at certain stages to take out certain mineral and additives, and then running it through an ultraviolet light system. The unit we had installed was developed for NASA and Carl Parsons happened to buy directly from the designer."

"We both feel better, but maybe it is psychological," Tom said.

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Ruidoso couple runs house with rainwater - Health issues drove them to alternative source and treatment system