When we replaced a 16 year old water heater this spring, we went with the GE heat pump water heater (Geo-Spring?). Although it includes resistance elements for backup / supplimental heating, I set it for e-heat mode which prevents the heating elements from ever coming on.
I have the same 50 gallon GE water heater and use it in e-heat mode also.
If the ambient temperature around the heater goes below 40 Deg F, the heating elements will be used, it might stay in that mode for hours or days until it warms up. I have never seen it go into that mode in my house, but I don't live somewhere too cold.
It certainly saves us money on our water heat and we converted from propane.
To the original poster, tankless heaters are for convenience (space saving and unlimited water) only, not for saving money. For a house where someone lives alone, that has to be the most inefficient way to heat their water.