Are you in a hot climate? If so, go with a heat recovery unit on your AC.

I would have to say it depends on your hot water usage. If you use a lot of hot water and live down south I would agree with Gary along with a storage tank. If you live in an area that has more heating demands I would check into a heat pump water heater in comparison to an on demand. If you price an on demand I would make sure your breaker box and entrance cable will support it. Many people are priced an on demand unit that will supply the whole house (baths, dishwasher, washer) everything which very few can without having a breaker box upgrade and entrance cable which can be very costly. Count the times your home runs everything at once and check how much amperage you need to do that compared to supplying one bathroom plus maybe a dishwasher or washer. There are few hot water heaters that will allow everyone to take a bath while everything else is going anyway so why is there suddenly a need for both bathrooms to be running at the same time?

One other alternative is the marathon hot water heater (Rheem) which has a lifetime warranty on the tank which is a poly tank with extreme insulation compared to most water heaters. These are up there in the price range but also have a lifetime warranty on the tank which if in a basement that is partially finished it might rust out in how many years?? NEVER which is something to strongly consider.

Your choices are all in the 500.00+ price range

Heat pump water heater- most expensive alternative but cheapest to operate year round unless you live in the deep south. Other countries have used them for years.

Waste heat recovery... free hot water other than the circulating pump cost and better efficiency on the a/c but needs a storage tank to really work the best.

Conventional lifetime warranty tank style- only 100% efficient but no worry about the tank rusting out and leaking. Price is a little hefty up front but there are rebates from most utilities.

Instant on- Very nice no reheating water but if you oversize the unit and need the entrance cable and or transformer upgraded the cost can be staggering and then there is the upgrade to the breaker box. This can be the middle of the road on choices or by far the most expensive.

I can't say there is any right or wrong decision. There are so many variables to look at and into before making a decison like cost per KWH, home location, family size and usage demands along with many others.

Best of luck!

Mo, have you taken notice how electric tankless heaters somehow dodge the federal yellow 'Energuide' label ALL other big appliances have?

I have never seen one with a energy sticker or energy star rating. I did the research and do not see it cost efficient to put one in my home.

Mo, I'm wondering how they dodge that sticker requirement...thought it was federal law....

I got off base from the OP with propane use for water heat other than a possible heat pump WH. I would have to say with gas involved I would really consider the tankless unit in comparison to a heat pump water heater.

Gary,
I do not know why I haven't located a sticker. I can't have a electric tankless because I don't have enough capacity left in my breaker box to run one that would supply one bath. I know that the 110v units work pretty well for bathroom sinks in some small shops that do not get a lot of restroom use and the water temp gets warmed up to 70 or so degrees in the building.

Thank you for your input. We live in middle TN. It can get pretty hot and humid in the summer time.