I don't even think in terms of 'general' because as it turns out, there is no general anymore. I don't know about the difference between male head of households, and female head of households - I don't think we have enough data to compare.
But, I'm damn sure that a single head of household deal tends to work out much better than a two head of household deal. And that confusion and constant power tripping is far, far better then a no head of household household. Damn Skippy about that one.
At some point someones' got to make a decision. I've always been in the 'don't be that person' camp, but if I have to, I will. Always fighting about who is making the decision is not efficient, and not making a decision is almost always a bad idea. So there has to be a process of arriving at a decision in relationships.
However people choose to work that out in their relationships is up to them in mutual consent. If that's met - if both sides consent to it, them I'm down with it, pretty much no matter what their doing is OK with me, I'm groovy with it. After all, relationships can be defined in different ways, and all of those ways have succeed. And all of them have failed too. So there you go. You pay your money and you take your chances.
The deal I had with my ex went: I'd make the big decisions, she'd make the little decisions. But, the decision as to what is big or little, was in and of itself, a little decision. We make a bit over 20 years that way, not too bad.