Some men, yes. Some men, no. Also, some women yes, some women, no. I don't see a difference in parenting skills between men and women. Generally, people are people and the degree of parenting skills they have is generally a result of the type of person they are.
You, my friend, are Naive. I appreciate what you are saying, but I'm afraid most children can see a SIGNIFICANT difference in the way they are treated by their mothers and fathers.
The most important point is that having two loving and involved parents is the best situation for a child.
I agree fully on your last point. I do see a difference in how I was treated by my two parents, however, I see that difference as more of a social construction. They both came from traditional families where these norms are solidly enforced, so I learned manly values like responsibility, hard work, etc. from my dad while I picked up stuff like compassion and generosity from my mother. This is because that's how their parents treated them.