Great question Peter. Water Heating is a very contentious issue that involves many different opinions and products. Being the 2nd biggest energy user in most homes it deserves a lot of attention and careful consideration. Every situation is different and a compelling case can be made for almost every product and situation.
Tankless Electric are NOT green or a good choice (except for serving one, lone fixture perhaps).
Tankless Gas/Propane atmospherically vented are usually not a good choice. (for concerns of IAQ)
Tankless Gas/Propane sealed combustion(with no pilot light, preferably condensing type) is the only type of tankless to consider but we feel they rarely make sense.
Most independent, well respected studies find that the payback for tankless are 20 years or more: Not cost effective. Other problems: Existing homes often need new infrastructure, more maintenance, most dont work with low flow fixtures, cold water sandwiches, lost supply during power outages, dependence on a non-renewable resource,a possible increase in overall energy use due to endless supply.
Many Energy Efficient experts prefer tank to tankless and most are now advocating Heat Pump Water Heaters which are the future of water heating. With efficiencies from 125-300% these water heaters often use less energy than the most efficient sealed combustion gas models.
Generally, with existing homes its best not to change existing infrastructure and simply upgrading in efficiency when its time for replacement makes the most sense. For new, homes we use solar with electric tank backup but will probably be switching to Heat Pump Water Heaters, whenever possible moving forward.