Will depend on the period of time and where/how it’s driven. If it’s one week, then the energy used to produce the battery for the electric car will probably be more than any savings. If it’s 50 years, mostly town driving or in rolling terrain with bursts of acceleration and braking, then probably the electric car will be more efficient because a large power station has greater thermal efficiency than a small internal combustion engine and electric vehicles use regenerative braking (i.e. KERS), so the cycles of acceleration and braking will really punish a regular car.
If it’s doing long trips down an autobahn, then the electric vehicle won’t have such an advantage because there would be very little braking, you’d have to stop to recharge really often, and the battery would probably need replacing every year (hence energy costs in recycling the battery).