It's difficult to understand the fascination with "efficiency", particularly for hunting rifles which in most cases are fired fewer than 1000 times by their present owner.
Powder costs less than a penny a grain, yet decisions are made on that basis.
Of course for a given bore diameter a smaller case will use less powder to reach the same MV as a larger case, but the larger case will always reach that same MV at a lower pressure. Most importantly, if pressure limits are to be respected, the larger case will be able to safely generate higher MV's.
We all know too about diminishing returns. The 22 LR can generate about 1500 fps with a tiny payload, the 223 can generate twice that with 10X the powder, and the 220 Swift less than three times that with almost 20X the powder. So if you only "need" 1500 fps, the most efficient choice is the 22LR, but what's the most efficient if you need 4000 fps?