For my husband and I, as far as "responsibility" goes, he never makes a decision without my input. Its kind of like, the default setting is: let's talk about this and make a decision. Once in awhile, one of us feels strongly enough about something that we just go ahead and do it.
But there's a respect there, I would never make a decision I thought my husband wouldn't agree with, and vice versa.
Once in a blue moon, however, I just don't want to be the one to say yay or nay. That's when I ask him to take the lead.
This is why I said there isn't any set way to do it. It could be your wife trusts your decision making skills better than her own. It takes maturity to acknowledge that, and if that's how she feels, it may work better for you to take the lead.
Take it in prayer, my friend.