Gas. (Actually, here in the rural mountains, propane.)
Ok; I went ahead and did the spreadsheet (all amounts are in US dollars or are US measurments). Work can wait, this is more important. The first time I filled the tanks after moving here was in October of 2004, and the water heater was replaced in March 2005; so I don't have available information to do a summertime comparison. The winter comparison is compromised by the fact that I heat the house with gas, and by the fact that it is difficult to know which winter was colder. Still, the spreadsheet suggested a 16% fuel savings, which was about .44 gallons a day. At about $2.00 a gallon (that's for propane; natural gas and electricity are probably much more), that's around $300 a year. However, a tank heater doesn't work as hard in the summer as in the winter; so let's say $200. So if you had to buy a new heater anyway (I did, my tank died), you take the marginal increase in the cost of a tankless heater over a tank and divide that by the annual savings. This seems to suggest that my tankless heater will pay for itself in about four to five years. Again, my calculations are not highly accurate and could be off by a considerable amount. When I was researching prior to purchase, my estimate then was a payback period of five years; so my current estimate seems to be in line with my expectations. Note: your mileage will vary!! Besides the tangible financial benefits, there are intangible benefits as well. First, you're burning less fossil fuels and therefore making a contribution to the preservation of the environment which sustains us all. Second, you're burning less nonrenewable resources, the demand for and control of which are causing governments throughout the world to become increasingly stressed; thus you're making a contribution to world peace. Third ... endless hot water in the shower!!!