Clipless. The way to not have your feet bother you on a long day is to pedal all the way around the circle, i.e. hardly push down at all. MTB shoes on SPD pedals. Plus a pair of trail runners for off-bike fun. I especially like Shimano PD-A600 pedals for their large support platform.

Efficiency is a red-herring because the definition is maleable. The big reason for clipless, and toe-clips before them, is that you use more of the muscles in your legs, hence each individual muscle takes longer to get tired. I.e. your legs last a lot longer and you'll feel better the next day.