Interesting article about peak vs. off-peak load, but the original question was about NG tankless water heaters, not electric.
I bought and installed a tankless natural gas water heater 2.5 years ago when my wife and I bought our first house. We love the thing, but it does require minor adjustments to lifestyle. We went with a Bosch unit that does not have a pilot light, but uses 2D cells to spark a pilot before the main burner is lit. Since we installed it before we moved in and therefore had not established a gas bill base-line, we don't know how much we saved. The old unit was a 1977 AO Smith 40 gal tank and I was afraid it'd fail as soon as we moved in, so I did it while we still had hot showers at the apartment. We have compared gas bills to the people before us, but I think they kept the thermostat at 78 with the windows open all winter, because we use far less than half the gas they did (and I'm not yet heating with wood, though I hope that changes in the next few months).
Expect to wash your hands with cold water unless you want to run the water for 60-90 seconds before you wash. We just wash our hands in the cold, but some guests who don't know are confused why cold water comes out, no matter which handle they turn! This is because the heat exhanger does take some time to get hot enough to heat the water, then for that water to be piped to where you're using it. Insulating the hot water pipes helps the heated water to not dissipate the heat around your basement or in your walls, but doesn't make a huge difference. Once you have hot water at your tap, though, it is endless. Our system is made to handle only one major hot water usage at once, but I've showered hot with the clothes washer using hot water and not had any problems. The one thing is with appliances that INTERMITTANTLY add hot water, it might not work as well, since the burner goes out every time the demand for hot water stops. We have problems with our dishwasher not rinsing all the soap residue off in winter. We've had no problems with laundry, though. (DISCLAIMER - It may just be that our dishwasher just sucks. I didn't research that unit because it came with the house)
The other advantage is that water keeps moving through the unit and doesn't significantly deposit minerals there, so if you have hard water, the life expentency of the unit is much longer. My dad's hot water tank fails about every 7-8 years, no matter what he buys. I think the longest lasting one was 10 years, which is too short for me. Time will tell if I made the right choice, but I'm pretty confident I did.
Overall we're very pleased. We replace the D cells when we call for hot water and it never comes, and it's right back.
If it is more efficient, lasts longer, AND enables you to move ahead with your woodburner install, how can you go wrong?!?