Instant, or tankless, water heaters are great. We sell them and I have one tied to my solar storage tank. Read on...
If you don't use any hot water, the tankless just sits there and you don't pay for any energy. On the other hand, if your hot water demand is such that your conventional heater just barely keeps up, the tankless does not save you a single cent. (Your conventional becomes a heat-on-demand.)
So the amount of energy the tankless saves depends on how much hot water you use. Consider this:
It takes one Btu to raise one pound of water one degree Fahrenheit - no matter how you heat it.
If you heat the water and then STORE it, there will be losses as heat leaks from the tank.
A tankless heater does not store the heated water - thus the savings.
The tank loss is ALL a tankless heater saves.
An extra insulating blanket will GREATLY reduce the tank losses of an electric water heater. (Not as good for gas because the flue pipe allows heat to escape up the center.)
So, if you use very little hot water, a tankless is your best option (and solar is the worst). A weekend cabin or a vacation home are excellent applications. Because they can provide an unlimited quantity on demand, a tankless would be even better in a barrack. But in a residence with typical hot water usage, the tank losses are a small part of the total energy consumption. Tank insulation is a better investment than a tankless heater.
A tankless heater must provide those Btu's to raise the water temperature - and you must pay for them - with after-tax money. A solar water heater provides those Btu's from the sun. Yes, there are some tank losses - but you don't pay for those Btu's either. (And you can reduce them to almost nothing if you add some insulation.) And the money a solar water heater saves is non-taxed.
If you come to the Alabama Solar Technology Center, you will see a Takagi Jr. gas-fired tankless heater providing back- up to the 275 gallon solar storage tank. This storage tank provides radiant floor heating as well as hot water for general purpose use. During the winter - when we have several sunless weeks - the tankless heater provides the heat. Plans call for a wood-burning boiler, another renewable source, for winter back-up. But the Takagi is never going away.