A standard gas grill propane tank is 4.6 gallons. Here in Knoxville, I'm paying $3.60 per gallon at the local U-Haul (why U-Haul sells propane I'll never know, but it's close and it's handy) which costs about $16 per tank. I brew all grain and use the same tank to heat strike/sparge water and boil and I get about 3-4 brew sessions per tank (6 gallon batches). I think if I brewed 12 gallon batches, it would be a little more efficient.
Compare that to electricity. In Knoxville, I'm paying about 8 cents per kW-hr. It's hard to compare apples to apples here because electricty is a little more efficient (less heat loss). For this example, let's say electricity is 30% more efficient. Propane has about 84kBtu/gallon and I use about 1.3 gallons per session which is a total of 109.2kBtu's. A similar amount of electricity would be 76.4kBtu which equates to 22.4 kW-hrs. Do the math and you get the following costs:
Propane: $4.68/session
Electric: $1.79/session
This tells you that electricity is a MUCH better buy, plus, I think the 30% more efficient number is pretty conservative which further tilts the scales towards electricity. However, when you take into account the actual output of both sources - propane has a huge advantage. My burners are about 150kBTU/hr which equates to about 43,000 Watts. Even if electricity is twice as efficient, that's still over 20,000 watts of electricty needed to keep up with propane. Even with 220 VAC, that's a huge current draw for most households. That means you have to live with a reduced power output which means the brew day is longer.
Personally, I like speed. Speed is important to me, that's why I use propane. If speed isn't important and you'd rather save a couple bucks, maybe electricty is more suited for you. Some people brew in basements with little or no ventillation and can't use propane. In general, if you are brewing outside and don't mind a couple extra bucks per batch, it's hard to beat propane.
Natural gas on the other hand............forget it, that's another thread.
Prosit!