Is it true that a bigger engine can be more efficient given that everything else is identical?

[muflah]

So I was watching a review of an older generation Toyota Vitz/Yaris on a YouTube channel (car wow I guess) a while back and the reviewer said the 1.3 L variant can give a better mileage than the 1 L. He reasoned that since a bigger engine struggles less to get to a higher speed therefore burns less fuel thus is more fuel efficient.

Can we observe the same behavior in other models with multiple engine options or the reviewer didn't know what he was talking about?

[Hassan1991]

Well, kind of. However, there are additional variables.
For example, if a chassis is designed to be pulled by a 1.3-cc engine, then it will provide the best mileage with it. Whereas if you put a 1.0-cc engine in that same chassis just because of the taxes, then it will provide you bad mileage.

[ivtec3]

Yes its true. Power-to-weight ratio is the key indicator here.

Just like a Grande gives much better mileage than 1.3 GLi Auto with the same body shell. Same for 2.7 TR Prado vs 4.0.