When we lost our water heater in 2008, my husband, who is a mechanical engineer, did a cost benefit analysis of tankless vs. electric.
We have a 500 gallon underground propane tank and I wanted the former. He also included the handsome rebate given from Uncle Sam. After checking the specs on heat transfer efficiency (which he specializes in) for each type of unit and the cost off propane vs. electricity....the numbers showed that at that time (and still today in 2011)the electric water heater is not only more efficient, but more cost effective over an 8-10 year time period.
The tankless did have a payback period, but it was 8-10 years out. His determination also assumed that the unit never breaks during that time or needs servicing. My husband also looked at the robustness (is that a word?) of the design and decided he didn't trust the tankless unit would last.
The electric unit has it's element in direct contact with the water which is 98.9% efficient (heat transfer). A flame under a pipe is much less efficient (I forget the exact number) so you need more propane to heat the same quantity of water. I would have wanted a unit large enough to heat enough water to run the dishwasher and take a shower. We found if I also wanted to run a load of whites in the washer, I would need an even larger unit which gets much more expensive. So I would have less options for when I could do chores. I would have to be more conscious of what I was running and when. Plus, we knew we would probably move in 10 years and never realize any payback.
If you also need to install a propane tank and lines...well....we didn't do that calculation (as we already had the tank), but you can see that now your pay-back time is much much much further out.
I like the concept of the tankless and think it would work well in a cabin, barn or summer home, but for now, the power plants (which are only like 60% effiencient) can make and send electricity to your water cheaper than a flame in the shorter term. The well meaning folks selling tankless units were astounded when my husband showed his excel charts to them. If you trust the design and plan to have your property for many years (over 10), and already have access to gas, then you may want to try tankless. Be sure you get the right size for your needs.
I hope my two cents helped some folks. I would ask that you use your local electric and propane or natural gas rates and do your own checking to see how the two stack up.
We didn't look at the environmental impact. Some might counter that propane burns much cleaner than a power plant and that this is more important than the money spent. Can't argue that one.