Is the second floor really an attic or the first really a basement? Otherwise, if both are living spaces, I don't think I share your enthusiasm about insulating between them. Perhaps a better sound barrier may be useful sometimes but any effect on indoor climate would be very minimal. At the very least it would be much less comfortable than what a two- or multi-zone HVAC system would provide.
If both are living spaces, there is no vapor transfer between the two floor you would be concerned with and so vapor barrier direction does not matter if you are really doing it to improve sound insulation.Â
If the floors are not exactly living space, you would direct the vapor barrier toward the exterior if you're in a hot and humid climate and toward the interior if you're in a colder climate with a longer heating season.
Perhaps your situation is very specific and you want to post more about how the house is constructed?
