Differential size absolutely plays into mileage.
With everything equal or the same, besides ring gear diameter, the larger unit will get worse mileage. Larger parts, more mass, more friction/contact area.
Which is great for strength, but not economy.
My friends k5, dyno’d with 10 bolt (4.56 gears) and then with the 14 bolt semi float we built (3.73 gears) dropped about 20hp at the wheels. Of course the ratio change plays into that too.
If you put a 10/12 bolt and a 14sf next to each other, the 14sf is significantly larger/beefier in all regards.