Mixed sex units are a worst case for a women. Sure carrying gear designed for larger men causes more injuries for women. Sure dragging men is harder on a smaller women. Sure being accurate with a heavier gun (designed for a man) is harder.
But how about comparing male units with female units. Women are smaller, take less resources, can fit in smaller spaces, are easier to carry, etc. A truck/plane/boat/whatever can carry more women, and you need less food for each one.
I suspect women given the chance could cause problems for the male competition. Less ego, less er, male. Try some wargames between males vs females. Evaluate their strategy, handling stress, etc. If men are as bad as guessing women's strategy as they at predicting women's feelings they are in for a very hard time indeed. I've heard that men have a substantial advantage in a marathon, but are completely wasted at the end. Women take longer to get to the finish line, but are not nearly as decimated by it.
I seem to recall that NASA did a study and came to the conclusion that women were better suited for space. Just as smart, somewhat smaller, more finger dexterity, and consumed less water, oxygen, and food. This led to a rather unpopular conclusion that most astronauts should be female.
So sure, if your metric is bigger/stronger = better then yes men win every time.