I think that on average women are more prone to be aware of physical appearance overall, but I would not call that true vanity, more a matter of attempting to live up to cultural expectations. And while there are certain things that drive men in the same fashion, that is often more insecurity than true vanity as well. (Well, except for the constantly looking in the mirror part just for the sake of looking. That actually is vanity.)
Vanity is often a misunderstood concept, and I believe hinges on that someone wants to be beautiful for the sake of simply being beautiful, and then in turn hold that beauty over others. (It's more than beauty in truth, but that is the simplest metric to mention.) But most people who are supposedly vain are not attempting to be beautiful simply for its own sake, but seek to leverage it for other purposes such as social acceptance or finding a partner--that's not vanity, that's survival in a world of aesthetics.