In "Women are not men", a freakonomics podcast, you can hear lots about gender differences, including the ever growing slice that is devoted to studying gender differences in competitiveness (what a great topic:)
(see e.g. here, here and here).
You can listen to Uri Gneezy, my coauthor on the first gender and competition study, talking about it somewhere in the middle of the podcast... He also emphasizes his paper with Kenneth Leonard and John List: Gneezy, U, Leonard, K.L. and List, J.A. (2009) “Gender Differences in Competition: Evidence from a Matrilineal and a Patriarchal Society,” Econometrica, 77, 5, 1637-1664.
In the podcast you also find work on gender differences in online presence, Happiness and Crime...