Gasoline on the road versus coal/natural gas/etc... in a power plant, then transferred at a slight loss through the electric grid, transferred at a loss to charge batteries, then transferred at a loss again into mechanical energy. That is ignoring the additional problems with the complex chemistry, manufacture, and eventual disposal of batteries versus steel and aluminum engines.
Almost certainly not better when everything is accounted for.
Ok; lets pick that apart, only this time with actual knowledge instead of your "intuition".
First, Gasoline engines are around 20% efficient. That means you burn 5 gallons of gas and get 1 gallon of gas worth of actual travel. Plus, Gasoline cars do not have regenerative breaking (we'll get to that later).
Second, Electricity production using Natural Gas has 35% efficiency. So for that equivalent 5 gallons of gas, you get 1.666 gallons of gas worth of travel, but you have to add charging efficiency, battery to wheel efficiency and of course transmission line efficiency. I'll leave it as an exercise to the reader to look those up, but For rough numbers, the battery to road efficiency is about 87%, the transmission line efficiency is about 50%, and the charging efficiency is about 85%. There are some other minor factors, but the big ones above are the main items. So, you take and multiply all of the efficiencies number to get the final efficiency. With electric vehicles, that efficiency is about 13% all told.
So! now we know that gas engines really are more efficient! Not so fast, heres where that regenerative breaking I mentioned above comes into play. There is no known way to convert mechanical energy back into gasoline, but with an electric vehicle, the circuits to take mechanical energy and put it back into the battery when breaking are very trivial to make. That means that the amount of energy it takes to make an electric car with regen breaking go 1 mile is far far less than it is to make a gasoline car go the same distance when all other factors are included. This number is typically 1/4 of the energy on average. That means that of that original 5 gallons of gas worth of energy, the electric car only got .64 gallons, but that will take the car 2.58 gallons of gas worth of distance while the gasoline car only got a gallon of gas worth of distance. Regen breaking is the key folks, always has been. With electric vehicles, regen is almost automatically included. With all other types of propulsion, it is a nasty and complex problem that is usually solved by ---- you guessed it---- adding a battery and electric motor...