These seem to be getting a lot of hype as being energy savers but I think in the long run, they simply are not. I had a gas fired tankless water heater when I lived in Japan back in the 70's and I hated it. The temperature of the water depended on the water flow. Most of the time, to get the water temperature high enough to use, you had to turn the flow down to a trickle.
In this unit, the gas flame was constant, so the temperature of the water was determined by the amount of time it spent in the heat exchanger. The faster the flow, the less time in the heat exchanger. I'm sure the technology has improved since then, but as seen in other posts, there are still problems and the savings don't seem to be there.
I think one reason for not seeing the savings is that unlike a storage water heater, these are not insulated, so when the demand for the hot water is removed, the residual hot water gets cold fast and has to be reheated when there is a new demand. The cycling cost may offset the savings in storage costs.
In the early 80's, I had an electric water heater in a garage in Virginia Beach. It was an old water heater with no insulation. I did a loss calculation on it and figured the cost of storing hot water was running me around $9/month in January. I wrapped R-11 insulation around it and calculated the cost to be around $1.30/month in Jan. This was confirmed in my electric bills.
A well insulated water heater inside the house envelope (heated space) seems to be the best route as any heat lost by the water heater is retained in the house. Good in the winter anyway, not so good in the summer in the south.
Now, electric tankless water heaters are on the market. I teach a class at a couple of lineman's schools so I get to meet with them and hear some of their problems. These electric tankless water heaters always come up. Homeowners complain that their lights dim when ever someone turns on the hot water.
The reason that the lights dim is that the water heaters draw almost 100 amps, most residential distribution transformers are rated for 62.5 amps continuous. They can handle over 100 amps for short periods of time, but their output voltage will drop from 120 volts to less than 100 volts in the process. One lineman said he measure 92 volts at the bushings (connections) on the transformer.
Often, more than one house will share a transformer so the dimming of the lights will not be welcome by the neighbors.
One thing the utility can do is install a larger distribution transformer, but that costs the utility a lot of money, not just for the transformer but also for the losses. There are two losses in a transformer, no load losses and load losses. No load losses are losses in the transformer when it is energized and is caused by the energy needed to magnetize the core. It is a constant value, its there 24/7 whether there is a load on the transformer or not.
The other losses are load losses and increase exponentially with the size of the load. A small transformer will have very high load losses when a tankless water heater comes on. A larger transformer won't have as high a load loss, but the No Load loss when the water heater is off will off set any load loss savings.
Residential customers do not see the effect of losses in their electric bill because the electric meter is on the secondary (output) side of the transformer. This is called secondary metering, the utility (actually all the rest of us in the form of higher rates) absorbs the cost of the losses.
Many commercial customers own their own transformers and get primary metering, that is the meter is on the high voltage side of the transformer. They get a better rate, but they pay for all the losses. I think if homeowners that buy a tankless water heater were required to be treated as commercial customers, that is they had to buy the larger transformer and pay for primary metering, they would soon see the real cost of these electric tankless water heaters, and its high.