Question:
Is there such thing as a home water distillation unit? Any specific brands?

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Answer: Why would you want a home water distiller?

If it is for purity for drinking, Reverse Osmosis has been shown to be much better. For one thing, volatile organics will remain pass through a distiller and end up in the product, such is not the case with reverse osmosis.

Distilled water IS useful for topping up batteries and irons, but not for drinking. It tasts lousy and it ISN'T necessarily clean

Typically, the better the reverse osmosis water, the lower the yield, other things being equal. Elevated pressures allow more stuff other than the water to come through the membrane. There are, of course, issues about the membrane technology, but I don't have the expertise to comment on that, or to provide hard numbers of any serious kind. Some membranes are better at rejecting the organics than are others.

I have no idea what the state of the art in reverse osmosis is, particularly for home use.

We use a reverse osmosis / ion exchange / charcoal system to purify water in the lab. The reverse osmosis system produces about 50 kilo ohm water, which still contains chlorine, trace organics, and significant amounts of minerals. After removal of the chlorine and the organics by the charcoal, and demineralization by the ion exchange system, we get 18 megohm water, pure enough for most lab uses.

Our RO system delivers about 10 % of the water. The rest gets passed through as waste. We use between 50 and 100 litres of good water most days, so we waste between 450 and 900.