Men have to work to improve the quality of the woman they can attract, while women need to work to maintain the quality of the man they can attract. Men are constantly trying to attract the best of the opposite sex, while women are constantly trying to stay with the best of the opposite sex. For a man, this means improving his character and appearance so that he is as attractive as possible to the women that wouldn't consider him otherwise. For women, this means improving her appearance and character so that she is as attractive as possible to the men who already want to sleep with her, but as of yet do not consider her for a relationship or marriage.
"The upper hand" is usually touted as an advantage that men have over women, and in one sense this is accurate. Because men care less, they can afford to be more cavalier, knowing that the girl is more invested in the relationship and therefore more willing to tolerate behavior from him that she dislikes. But while the advantage is real in this respect, there are two important things women should know about it.
1. The man's "advantage" is one over which a woman has direct control. By not initiating, or giving it up easily, a woman can filter out the men that just want sex, and avoid investing too much emotional energy in dead-end relationships. This energy can instead be spent improving herself, and therefore her "league" or dating options. In fact, by the very act of acknowledging her own (current) limitations and not wishfully giving in to a man just because he is hot or rich or famous, a girl instantly and significantly increases her attractiveness. I've met a number of girls that I can tell would like to date me, but are also smart and confident enough to recognize and admit to themselves that I am not (currently) interested in dating them. These girls do not play into my attempts to have sex with them. I have a lot of respect for these girls, and respect matters when it comes time to choose a girl to get serious with.
2. The man's "advantage" isn't as great as it seems. A man's hyper-sexual mindset is not without its faults, but a couple of those faults are perhaps less obvious than the others. The first is that, while the desire for sex leads to the upper hand in relationships, and while the upper hand does bring with it a certain power, this power only exists because the man is playing below his league. A decent analogy is an 17-year-old acing the 5th grade. Sure, he gets straight A's and can dominate the little 10-year-olds in gym class, but his successes are hollow because he always knows he should be in the 12th grade. His victories serve more as a reminder that he is not reaching his potential than as a reflection of his true abilities. In other words, the upper hand - the man's supposed advantage - is necessarily accompanied by a state of perpetual dissatisfaction and a reminder of his underachievement in what is (for most men) the most important arena of his life. You can be sure he is both aware and unhappy about this, just as much as the woman is aware and unhappy of the fact that she has "the lower hand." It is a bad situation for both parties. The second negative aspect of the phenomenon is that getting a girl in your own league is a hell of a lot harder for a guy than you would think, because all of the girls in his league are busy fucking the men in the league above them, or yielding the upper hand in relationships to them.
As I said at the beginning, these are generalizations. There are obviously instances of women having the upper hand in relationships, and in these cases, since the roles are reversed, so are the effects. And as I also mentioned at the start, the phenomenon occurs in various degrees. In these cases, the effects described above occur in proportion to the discrepancy between the value or "league" of the man and woman.