Just an opinion, all else being equal
The skipper is the one who is calm, cool, and collected in emergencies. The skipper is not the one who freezes up and can't communicate or decide when the crap hits the air and the chips are down.
The skipper is the one who commands, not requests, in emergencies. Choose for that trait of save your boat by committee.
It helps if the skipper knows what they are doing, which is why I say all else being equal, but you can be a licensed master of the universe and if you freeze when a sheet releases, shroud pops or water appears in the bilge you are a useless skipper more liable to harm than help.
That's why I'm the skipper, and my wife is along for the ride, and that's ok with both of us. What I am having a little trouble with, is teaching her what to do in an emergency. She runs the jib sheets ok, but is just terrible at the helm, and is not getting much better with practice, she freezes when something goes wrong, and is slow to react when told what to do. Before every sail I remind her what to do if I fall overboard. (release both sheets, try to steer into the wind and wait for me to swim to the boat if I'm able to, if not, call for help) So what I do is prepare the boat as if I'm single-handing it all the time.
We are still new at this and it's likely I just picked it up way faster than she did, so more patience is needed, and I am giving her more practice at the helm. We have only been out maybe a total of 20 times, so there is a lot more learning to do.
But as for who is in charge...
I AM THE CAPTAIN