Propane is a first energy source, whereas electricity is a secondary energy source. This means you can use energy from propane directly. On the other hand, electricity has to be generated from a primary energy source, like coal, natural gas or petroleum, before it can be used. Also, propane is measured and distributed in gallons and BTUs (each propane appliance consumes a certain amount of BTU/hr); electricity is measured and delivered in kilowatts (each electrical appliance consumes a certain amount of kWh). One gallon of propane delivers the same amount of energy as 27kWh of electricity.
Sources of electricity production
Propane and electricity: which is cheaper?
Whether propane is cheaper than electricity or vice-versa depends on several factors. First, it depends on the market prices of electricity and propane. These vary depending on where you live: propane, for instance, is more expensive if you live relatively far from a supply source (the Gulf Coast and the Midwest) or if the price of crude oil is high since it is a byproduct of natural gas processing and crude oil refining.
At a given time, you can calculate which energy is cheapest by looking at your bill and using the 1 gallon of propane = 27 kWh of electricity conversion. For example, if you are paying $2.4 dollars per gallon (November 2012 US Energy Information Agency price) it is equivalent to 8.8 cents per kWh of electricity. For November 2012, this means propane is cheaper than electricity on average since electricity retails at 11.61 cents per kWh (US Energy Information agency price).
To give you an idea of what this means: At this rate, somebody who showers, cooks and washes dishes once a day and does their laundry once a week uses 33 gallons of hot water a day. At US Energy Information Agency prices for November 2012 they would spend around $357 for electricity or $288 for propane per year, so save $69.
Propane and electricity: which is cleaner?
Lastly, contrary to popular belief, electricity is not a cleaner source of energy than propane. In fact, 49% of electricity in the United States is produced from burning coal as the primary source of energy. And coal emits far more carbon emissions than propane. So depending on the energy mix in electricity, propane can actually be significantly cleaner than electricity.