Start talking the fuel economy of different petrol engine types and designs and things get complex, fast. Amongst other factors, fuel economy is affected by internal friction, pumping losses, combustion inefficiencies and the air/fuel ratio that is used.
The biggie with internal friction is, literally, how big the engine is. A larger engine has longer internal bits rubbing other bits, and so a 5.7 litre V8 is always going to have poorer fuel consumption that a 2-litre four cylinder. That statement applies when both engines are producing the same low power required for cruising, but may not be the case when the power demand is high – climbing a hill while pulling a trailer, for example. In the latter situation, the smaller engine will have to rev very hard to develop adequate power, and the higher the speed of the engine, the greater the power loss through friction. Because of the high loads to which it is being subjected, the small engine might also move out of closed loop (ie ~14.7:1 air/fuel ratio) to a much richer mixture. So as the power demand increases, the practical on-road fuel consumption may not so clearly favour the smaller engine over the larger engine.
Another way of seeing this is to look at the fuel economy gained from a small engine car that always has to have the ring driven out of it to keep up with traffic. In this situation, the fuel economy is often poorer than the larger engine car that is always just loafing along.
Pumping losses refer to the drag caused on the movement of the pistons on their intake and exhaust strokes. Any restriction on the intake – including, critically, the partly closed throttle – will lower the pressure of the air that fills the cylinder on the intake stroke. Rather like drawing down a syringe that has the needle opening blocked, power is needed to overcome this partial vacuum. On the exhaust stroke, anything that restricts flow out of the cylinder – from a poorly flowing muffler to bad port design – will again require power that’s subtracted from what is available at the flywheel.
Some BMW engines dispense with the throttle – and instead change intake flows by varying valve lift and timing – however the intake pumping losses remain. (Diesel engines, of course have no throttle and so much smaller pumping losses.) A better approach to reducing pumping losses is to adopt the Atkinson or Miller cycles, where the closing of the intake valves is much delayed at lower engine rpm. This poorer intake flow requires the driver to more widely open the throttle for a given power output, so reducing pumping losses. However, the engine also develops less power because its volumetric efficiency is much lower than an engine with conventional valve timing. Atkinson/Miller cycles are therefore used only when there is forced induction at low revs (eg a supercharger as in the Eunos 800M) or power is available from an electric motor (Toyoya Prius and most other current hybrids).