It's pretty much the same as RO water ... different filtration method, but similar in result. Distillation removes sodium and other common unwanted minerals but leaves some behind, RO removes chloramines, but leaves some sodiums behind. Take your pick.
Result is cleaner water, either way.
RO is the one apparently, but distilled looks like a good second-best.
I'm messing about with filtering rainwater at the moment ... has a trace of carbonic acid in it though. Certainly arrives at the correct pH ...!