Will an electric water heater definitely cost more than a gas one? On your utilities bill.

Most likely but you should tell us your current rates for both. I have two homes and one of them the electric rates are triple that of the other. It has been my experience that people who install electric water heaters just done have access to gas. Propane is quite a bit more than natural gas.

Here is a energy calculator, plug in the costs for each source of energy in your area to help you compare:
Energy Strategies: Energy Cost Calculator