Most electric fireplaces have a couple of settings so you can increase their efficiency. Some operate at two levels of heat, depending on how warm you want your space. And some allow you to turn on the fire without the heat, so you get the attractive look of a fire at much less cost.
Electric fireplace inserts have an advantage over wood fireplace inserts because there is no need for a flue going up the chimney. You can close this off for an electric fireplace insert, which eliminates heat loss up the chimney and increases the heat you get for your money.
If you spend most of your time in a family room with an electric fireplace insert, you can turn down the heat in the rest of the house and turn on the fireplace. This way, the room you're using stays nice and warm while you save money on heating the rest of the house.