I figured the gas vs electric cost vs the local REMC yesterday for a customer. Power is 3.35 times the cost of gas BTU to BTU.
For resistance heat, you'd need to give the electric company about 10% advantage on efficiency (100% vs 90%) so the true cost differential would only be about 3.0 times as expensive.
If you are talking about a heat pump though, it's going to be completely different. If I was dead set on electric heat, there's no way I'd try to do it with anything but a heat pump. The newer high efficiency ones have very impressive spec sheets.
Phil
p.s. To answer the OP post 1 BTU = amount of heat requried to heat 1 pound of water 1 degree Farenheit (at set conditions). There is no difference between an "electric" BTU and any other British Thermal Unit. However, to compare apples to apples you need to make sure you are comparing the output BTU's of both pieces of equipment, as fueled equipment will have an output BTU lower than the input BTU. The ratio of those 2 numbers multiplied by 100% is normally called the "efficiency" of the unit.