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Mufti Shafi' states in Ma'riful Qur'aan:

The Qur'anic Eloquence in Describing the Precedence of Men

It is noteworthy that the Holy Qur'an, while giving the first reason for the precedence of men, has not opted for an expression like "faddalahum alayhinna" ('because He made men excel women'), On the contrary, it has elected to give a deeper significance to the statement by using the expression: "Ba'dahum ala Ba'd", that is, 'made some of them excel the others'. The wisdom here is not difficult to see. The Arabic expression "Ba'dahum ala Ba'd" has a subtle indictation to the fact that men and women are part of each other. Therefore, there is a hint that the precedence of men, even if proved in one or the other field, will not go beyond being similar to the precedence of man's head over his hand, or of his heart over his stomach. So, just as the precedence of man's head over his hand does not diminish the role and the importance of the hand, similarly, the precedence of man does not cause any lowering of the status of women, because both of them are parts of each other's body - if man is the head, woman is the body.

Some commentators identify yet another hint here. According to them, this precedence men have over women is in terms of genus. As far as individuals are concerned, it is quite possible that a woman may excel a man in her qualities and practical accomplishments, so much so that a woman may be superior to some individual men even in the qualities of a care-taker.