I don't know, to be honest.
Looking at the fuel use first, heat engines like the internal combustion engine are not very efficient (this guy https://en.wikipedia.org/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot worked out why). So if we run a car on fossil fuels it will simply waste most of the energy in the fuel which would have stayed in storage if we hadn't pumped and refined it. Electric motors are much more efficient. But the efficiency of the electric power plants and distribution will range from perhaps worse than internal combustion, if they're fossil-fuelled, all the way up to very high, if they're solar-powered (in the case of solar power the sunshine comes for free and would be 100% wasted, heating the earth, if we didn't turn some of it into electricity).
Then there's the question of whether building an electric car takes more energy than building an internal combustion one. I would guess that it might at the moment, given the energy needed to make batteries. But I am guessing. And I haven't factored in any future improvements as the battery stock becomes large enough for recycling to start having an impact.
To be honest the arguments against fossils aren't usually energy related. They're usually based on a) the bad effects of CO2 on the climate, b) the bad effects of exhaust pollutants on health and c) the fact that sooner or later fossil fuels will run out.