It is known that hydrocarbon powered cars typically turn chemical energy into mechanical motion at about 35% efficiency (45% for Diesels). It is known that large power plants generate electricity from fuel at about 50% efficiency. The process of charging a battery is about 75% efficient, turning electrical energy into chemical energy. The reverse is also true, for battery discharge (75%), and the electric motors of an electric car are about 95% efficient. We multiply these numbers to get the overall efficiency of conversion of original fuel energy into mechanical motion for the car: about 27%. Even allowing for regenerative braking energy-recovery, it looks like ordinary cars win the efficiency thing here. We need better than that!
Traditional cars and power plants don't use the same inputs. Even if electric cars are less efficient, they can potentially be powered by renewable energy sources rather than hydrocarbons.