Is reusing bones for stock better than once cooking longer with more water? I've heard about reusing bones for stock (eg. blog post even if the second time is a bit weaker flavor.

My question is, if there is some advantage to this. Consider the following to scenarios: 


Fill pot of bones with N liters of water until just covered. Boil X hours. Strain broth. Refill as before. Boil X hours again. Repeat. Combine all three batches into one big soup.
Fill pot with 3N liters of water and boil for 3X hours. 


The former seems much more labor intensive. Will the flavor extraction work better the first way for some reason? Perhaps the fresh water is better suited for extraction? Perhaps the lower water:bone ratio helps speed things up?
I would think this would result in thin stock under normal circumstances. I would go for a longer, single boil instead if the fear is there is remaining goodness in the bones.