Electric heaters are virtually 100% efficient. The electricity all goes to heat. Arguments can be made about the value. In most places, gas is cheaper to buy, but for efficiency, electricity will win.
While true, I can see why some might have trouble seeing it. The important thing to remember is that we are comparing your billed costs for electricity and gas which are based on your consumption as measured at your meters. The measured electricity consumption resulting from the use of your electric heater is indeed virtually 100% efficient. On the other hand, the measured gas consumption must be converted into (usable) heat through a furnace that is somewhere between 60% to 95% efficient.
What this analysis doesn't capture is the efficiency of generating the electricity being delivered to you. This can become a confusing discussion when considering all the different sources (e.g. solar, wind, nuclear, fossil fuels). For "apples to apples" let's just consider gas-fired generation. Its efficiency is somewhere in the neighborhood of 40% to 60%. Looking at it this way, an argument can be made that a gas furnace is more efficient than an electric heater fed using gas-fired generation in the sense that the former uses less gas than the latter.
The same applies to any heating applications, including water heaters, ovens, and cloths dryers.
The thing you have to remember with electric heat is that even though it's 100% efficient, you are also in essence paying for all the transmission loss on the wires between the power plant and you... and that's a very large number.
No, not really. Transmission and distribution losses are in the range of 5%.