There are a lot of factors that go into how "pure" water is after a treatment. For most purposes, RO or distilled water is your best choice to use on batteries. Some wells produce very "clean" water - these are typically very deep wells, but not always. There are, however, some very deep wells that produce "dirty" water. As for RO water, the purity depends on the membrains used and the prefilter. The RO can also have multiple passes (not typically seen in residential and most industrail uses) that purify the water a little bit more during each pass. The more passes, the better the water - usually...
As you can see, there are a lot factors that go into make water "pure. " Use what you think is the best - do a little research on the web on each of methods used to educate yourself on the different methods, and you'll be in good shape.
IMHO, distilled water from the store offers the best water for the price - less then $1 for a gallon. RO would certainly be a close second, but with them sitting side-by-side on the shelf and at usually twice the price, I'll stick with the distilled (the reason for the price difference is that the RO produces much more brine during the process so it take a whole lot more water to make water, plus the cost of large RO units is pretty high).