I think that I have seen studies in the past, but I do not have the references, sorry. If I see anything, I will try to post again and give you links.
We have had the Melody for about 1.5 years now, and we do love the taste of the water. It just feels very good. The issues that I have with it are that it doesnt really remo ve chlorine and flouride, like distilling does. You can, however, get filters for before and/or after to remove most of these contaminants.
If cost is a huge factor, then I would suggest using distilled water, then using "Prill beads", which will also ionize, alkalize and structure the water.