Physics suggests that its easier to pull vs push, but based on specific conditions and assumptions. Depends on the vector of the external force of the push / pull and where and how it acts on an object.
I believe in a motorized wheeled vehicle, its not nearly as significant, especially since the rotational torques are being transferred to the ground at around ground level with mostly tangential forces.
Assuming we are comparing as much apples-to-apples as possible (same weight, power, etc.)...
What will play a significant part in this will be the engine/drivetrain layout.
Anytime you have gears, coupling, or joints, you will likely be losing efficiency.
A Front Engine FWD car will have a transaxle.
A Rear Engine RWD car will have a transaxle.
A Front Engine RWD car will have a transmission, driveshaft, differential, and axles.
Engines laid out on the same side as the driven axle can reduce the number of couplings and joints like the driveshaft+universal joint and will use a transaxle which is basically a transmission and differential in one. This reduction helps eliminates some of the potential mechanical waste and makes it more efficient.
Manual vs automatic transmission matters as well as the specific design and how each is operated.
AWD or 4x4 drivetrain layout inherently suffers even more mechanical losses due to the extra transfer case/differential.
Aside from the mechanical losses in the powertrain, losses to efficiency will occur from not being able to put power to the ground = tire slip.
Again, cars with engines laid out on the same side as the driven axle will potentially benefit more because having the engine on top of the driven axle results in more weight on those axles, which means increased potential grip for those tires, effectively reducing the chances of tire slip.
Having the engine on the same side as the driven axle can increase gas efficiency and help increase grip to those wheels under "normal" circumstances but it also biases a lot of weight onto one side of the car. In more dynamic situations closer to the extreme limits of the car's ability to perform, having too much weight on one side can drastically affect the car's behavior (whether considered safer (for streets) or not depends on the behavior and perspective). On the streets, it won't matter nearly as much.