There's a matter, as you have identified, of real vs "lab test" benefits.
The REAL benefits of smaller engines, such as the 1.0 3-pot turbo in the octavia, are simply lower weight and less frictional loss (fewer cylinders). These are not contentious.
Petrol combustion depends on there being the correct amount of fuel and air (stoichiometric ratio) for complete combustion. The amount of fuel you burn gives you your power output, and the more air you can force into the cylinder (ie turbo) gives you the ability to burn more fuel.
The real question then becomes the thermal efficiency of the engine. Frictional losses can be included in that, but the claims of efficiency in turbocharged engines CAN be contentious. Manufacturers can write software that keeps the engine performing at its most efficient in unrealistic lab test scenarios (like the old NEDC fuel economy tests, where acceleration was 0-30mph in 27 seconds), but offer much more power (and thus burn more fuel) when you put your foot down in the real world.
Another approach (and one that has much better real-world results) is the use of faux-atkinson cycle. An otto cycle engine compresses the fuel/air charge, ignites it and expands it again. An Atkinson cycle engine expands the charge more than it was originally compressed - a proper atkinson engine has a very "interesting" crank setup to do this. Toyota typically implement faux-atkinson on their hybrids (like my GS) - the valves close late, so the compression stroke has already begun and some of the charge (air, since it's a direct injection engine) is pushed back out of the cylinder. The valves then close and the charge is compressed by the typical ~10:1, ignition occurs and the expansion is in the region of 13:1. This directly harvests more energy (and the end goal is to expand the charge until it reaches 1 atm pressure).
So, to summarise, for a given thermal efficiency the smaller engine has benefits in weight and friction (but the latter may mean that by default the thermal efficiency is slightly improved). Otherwise, for the same power output the same amount of fuel must be burned.
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