My humble opinion as an amateur player and coach, I don't observe any difference between girls and boys. As Judit Polgar said: “Whenever I speak to parents or to kids, I always encourage them that if they believe, if they do the work, if they are really dedicated, then they can do it. No matter whether they are a boy or a girl.”
Polgar sisters (2 GM and 1 IM) from one family has set up a great example for girls. With the determination of the parents and hard work of the daughters, they fought through all kinds of difficulties: communist government which setup all kinds of roadblock, travel limitation, limited resource, discrimination from male dominated chess community, pro-Russia FIDE ruling, tournament limitation (female were not allowed to play in male tournaments), and etc. All 3 sisters had beaten male GMs numerous times. Judit was ranked top 10 in the World for many years, and had beaten Nigel with a clean 8 win, 3 loss, and 5 draw record.
The problem is not about brain, it's about culture. Our culture doesn't encourage girls to be competitive and doesn't encourage girls to play chess. From beginner level to advanced level, girls population is much smaller than boys, and the difference increases faster when levels and ages go up. This leads to dramatic difference in the professional level. Only 2% GMs are female. I call this dummy result of the big number theorem, ie, when the base is large enough, there will be a few good one. Men just win the comparison by their much larger chess-playing population.
To change this, we have to make changes at the beginner level. That's why my daughter introduced NJ All-Girls Chess Camp last year with support from NJSCF, chess clubs, schools, parents and chess lovers. If you'd like to lend your hands, you can help fund the 2015 camp: http://www.gofundme.com/gcnj2015.