There are single point and multipoint heaters, the difference simply being whether hot water is supplied to one point or to a number of points in the accommodation. Regardless of this the economics of running a unit is governed only by how much hot water you use, the temperature of the water and the fuel used to heat it. The initial cost of the unit is also important, costs vary greatly and the price depends on the application.
The table below shows the cost of using 1000kWh, 3000kWh, 5000kWh and 7000kWh each year to heat water with three common energy sources for instantaneous water heaters, electricity, gas and LPG. 5000kWh is the average used by a family in the UK each year for hot water (All fossil fuel systems are assumed to be 90% efficient).
The graph below shows more fuels and assumes 5000kWh is used each year to heat water in a family home (All fossil fuel systems are assumed to be 90% efficient). It is unlikely that some of these fuels would be used in this way but they are included to illustrate how expensive they are. The graph is only accurate in the UK but I would imagine other regions would find costs similar.
The difference between the cost of electrically heating and gas heating is huge, and careful consideration should be made before deciding to buy an electric water heater. Electrical water heaters are usually cheaper but the price difference will probably pay for itself in running cost savings in a year. You may consider solar water heating but the numbers may not stack up in the UK, please have a look at this article. Solar hot water make a lot more sense in warm countries.
Clearly gas cylinders are very expensive but there is little choice in a caravan, apart from staying in a hotel instead!