When we were first planning our house I started researching on demand hot water heaters. The idea sounded great. You only heat water when you need it. They do cost more and there seems to be a lot of people on the internet who complain about the problems they have with theirs. We ended up going for it and getting a Rinnai 94i. We have had a couple of issues with it in the years that we have been using it. The first was that the incoming screen filter got clogged with sand and debris and slowed the flow so that it won't fire. I unscrewed the filter cleaned it and we were back in business. The second issue we had was that a bunch of snow piled up on the exhaust vent and blocked it. After sweeping it off with a broom it was working once again. Other than that I try and run vinegar through the system once or twice a year to keep it from scaling up.
The most load we have ever put on it was two showers and the washing machine at the same time and there was no problems meeting the demand. If you use low flow faucets and shower heads you could probably get away with a pretty small unit. I would think that most people would call a big hot water draw two people showering at the same time. If you had a 2 gpm head on each that would be 4 gpm if you had the water set all the way to the hot handle. Since you can set the temperature that you want with a Rinnai you could set the temp to 110 F and then go with just the hot handle. If you read their website the fine print say they assume a set temperature of 120 F that is mixed with cold down to 104F.
It looks like Rinnai now has an Ultra Series that are 96% efficient. If given the choice I would choose a smaller Ultra model. I wouldn't find it a big hassle to not start a load of laundry when two people were taking a shower but I think it could still manage that.
There is also an increase in lag time for the hot water to get to the faucet. It is not bad but it is enough that it is not really worth it to try and wash your hands with warm water. You will waste water waiting for it to heat up. It also depends on how far you are from the heater as with any house. If you are doing a sink of dishes then it is no problem to turn the hot water on and fill up the sink.
Noise is another issue to consider. It is a little noisy. Mine is located in the mechanical room that is attached to the outside of my house. I can hear a low hum when the hot water turns on. I would not mount this in an internal space like a pantry because it might be noticeably loud. If you are considering getting one I would find one that is installed so you can hear the sound and see if that is a problem in your situation.
We use propane to cook with and heat water. As a family of four with two small kids we use about 120 gallons of propane a year. That is about 10 gallons a month at around $1.80 a gallon comes out to 18 dollars a month. I really don't know what it would cost if these were both on electric.
Overall I have had a positive experience.