I haven't tested it side by side myself, but my reading says distilled is preferred. Not just for the lack of nutrients, but also for the lack of bad things in it like ethanol, and the higher pH than you see with wort/beer.
I don't think the osmotic pressure is much of an issue. Unless you're spinning it down and aspirating the liquid a couple of times, there will be enough residual liquid after decanting to add some ions to the water.