Electric tankless water heaters will reduce your electricity bill in the short term but are not as good for the environment, and make life difficult for the utilities managing the supply of power. For this reason these water heaters are losing ground in countries such as Japan where until recently they were the exception rather than the rule.

The main way in which on-demand water heaters save money is that in a tank water heater, you produce heat throughout the day for use later, and some of that heat escapes from the tank into the surrounding living space (or furnace room or wherever your hot water heater is located).

You can compensate for this somewhat by properly insulating your hot water tank (special insulating wrappers can be bought for this purpose - buy the thickest kind you can find), putting pipe wrap on your hot water plumbing, and by turning down the thermostat on the heater from the factory default of 140F to 120F, which is both more efficient and safer. But even with these changes you will probably find that an on-demand heater costs less to operate, at least in the short term, because there is so little energy lost to heat escaping from the device, since there's no tank for the heat to escape from.

The reason I say electric tankless water heaters are not as environmentally friendly is that they create random spikes in utility demand, which makes it more difficult for electrical utilities to manage the power demand. An on demand electric heater draws a huge amount of current while it is heating water. A tank heater, however, draws a lesser current for a longer time, and stores that energy as heat in the tank. What if in a city of a million, every home had an on demand electric heater, and everyone took a shower when they got up. The electricity company would have to quickly ramp up electrical production in time for the tankless electric water heaters to heat water for showers, then to quickly drop electrical production once the showering time (say, 8:00 am) is pretty much finished. Since they can't scale up this quickly with things such as coal or nuclear, they wind up ramping up much earlier (say, 3 am), and then have to ramp down much later (say, 10 am), so that although you may have saved money, you have indirectly required the utility to produce a significant amount of energy that isn't actually needed, and may go to waste.

For this reason, in Japan for example, there is a major campaign underway to convince people to move away from tankless electric water heaters, and instead use an electric tank heater with some intelligence built into it so that the tank heats water hotter when there is excess power on the grid, and then blends that water with colder water if required, to supply hot water at a steady temperature.

Note that in some areas you pay for electricity based on the time of day it is used, and in some states and provinces you even pay based on the peak amount you use. So if you shower at 9 am you are showering during 'prime time' for electricity prices, and that means an electric tankless water heater will cost you a lot of the higher-priced power, while a tank water heater, if it has the smarts built into it to know that little hot water is needed while you're away at work, can let out hot water stored up overnight, then not draw more electricity to heat the tank until the next night, when time-of-use prices have gone down.

The other thing to remember is the lifestyle changes you will need to make if you switch to an on-demand electric heater. The house I live in now has an on demand electric heater, and I must say it does not perform as well as I would like. The water flow is much less than you might get from a tank heater (because the tankless heater only lets out as much heated water as it can heat at that time), and for something like cleaning dishes, where you might turn the tap on, then off, then back on, then back off, it just doesn't provide hot water the way a tank heater does, because you experience a lag between when the water starts running and when the tankless heater starts heating. So your pipe is like a sediment core of cold and hot lengths moving towards the tap.

While on demand electric heaters are getting a lot of attention at present, and may become more common in North America in the short term, I expect their popularity will not last, because of all the problems described above, both to homeowners and electricity companies struggling to manage peak electricity load. If you're thinking about buying an on demand electric heater, be prepared to see short-term savings replaced with higher electricity bills in the long term, as utilities put more pressure on users to cut their peak usage, and don't be surprised if the performance of your heater isn't what you thought it would be, in terms of constant heat output or its ability to meet your intermittent hot water needs.