>what is the maximum nurse bee versus brood cell ratio in a big hive versus a small hive?
I think it's a matter of bees for that given valume and bees for the number of brood cells. If you have enough bees but too much volume they still can't maintain the environment. If you have the right proportion of volume, bees and brood it works well.
>The nurse bees only have to feed the brood that is not yet capped.
And warm all the brood that IS capped.
>Somehow, the small hive can curtail the queen to lay only so many eggs that the nurse bees can take care of them.
They do this by some combination of filling the cells with nectar to keep the queen from laying, eating the excess eggs and herding the queen around some. I've observed them doing all three at different times or in combination. Since they clean the cell for the queen, I also wonder if they "tag" it with some pheromone to let her know she can lay in it now? If so, they could just not "tag" as many cells.
>Unless the nurse bees go and eat the eggs that they cannot take care of.
They do sometimes.
>The limiting factor does not appear to be the egg laying capacity of the queen.
No, it seldom, but sometimes, is.
>I just think that it may be that small hives have better hygienic behaviour versus large hives.
I don't think so at all. I think the larger hive is more hygenic simply because it has more houskeepeers. The small hive has less varroa simply because it has less brood.