Are we talking laws of nature or influences from society? Regardless of either, I am thinking that women have more of a selection than men do, but ultimately the selective processes are different for men and women.
In laws of nature, I believe women are more selective. There are numerous studies done (google it) and documentaries that have shown that the reason why women have a heightened sense of smell is for this very purpose. Pheromones and such can tell a woman instantly if a man's genetic code will compliment hers to promote vitality and strength of the species. And yet, even with an intense physical attraction, a woman is less likely to pursue a relationship if personality and core values clash.
From a societal standpoint, I think men are far more visually selective than women. Though there are many women that swoon over a fantastic smile, that is not the reason they decide to date someone. Men see a woman that they are attracted to and if they choose to pursue it, they are more likely to start a relationship based on initial attractions.
There is always an exception to every "rule", however.