I am better at reading body language and subtle things. My husband is far better at big picture things and strategies. Just as one example. So when we discuss things we both contribute and we make a plan based on what we both know.
You’re right about the body language bit.
To my cost I have learned that I ignore my wife’s warnings about who is not to trusted at my own peril.
Now I listen.
I have often thought of it this way: one sex's strength is the other's weakness, thus as you say, "to complement each other".