Yes, of course. The efficiency of the use can vary considerably.
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Sow how does the efficiency of an internal combustion engine running on gas compare to an electric motor running off a battery?
In the US, the electric motor running off a battery mostly gets the electricity from a combustion engine turning a generator. Thus, it is most useful to follow the efficiency of the entire process of generating the electricity, not just the final use of electricity from a battery.
Even if you look at only the battery power from your electric outlet in your home, there are inefficiencies in charging the battery, not using the battery for some time, and discharging the battery. The motor itself likely runs at about 95 percent efficiency.
An IC engine powered vehicle is much less efficient than that. A rule of thumb is that a third of the power is lost in heat, and another third is lost in mechanical efficiency, leaving just a third to propel the vehicle. However, the electric vehicle also has losses in the powertrain which can approach the one third in the IC vehicle. It also must heat and air condition the vehicle, while heating is free in the IC vehicle. The battery must also provide lighting, battery and motor cooling and other electrical loads in the vehicle which decreases the efficiency more.