In common with many other raptors, female Peregrine Falcons Falco peregrinus are about 50% heavier than males. Their sexual dimorphism is thought to allow breeding pairs to exploit a wider range of prey through a division of labor: the male being able to catch more maneuverable prey species; the female capable of carrying larger ones. Given the difficulty of assessing the catch success and load carrying capacity of both sexes of falcon in the field, we here adopt a novel approach to test the division‐of‐labor theory by using a detailed physics‐based flight simulator of birds. We study attacks by male and female Peregrine Falcons on prey species ranging from small passerines to large ducks, testing how catch success relates to the flight performance of predator and prey. Males prove to be better than females at catching highly maneuverable prey in level flight, but the catch success of both sexes improves and becomes more similar when diving, because of the higher aerodynamic forces that are available to both sexes for maneuvering in high‐speed flight. The higher maximum roll acceleration of the male Peregrine Falcon explains its edge over the female in catching maneuverable prey in level flight. Overall, catch success is more strongly influenced by the differences in maneuverability that exist between different species of prey than between the different sexes of falcon. On the other hand, the female can carry up to 50% greater loads than the male. More generally, our detailed simulation approach highlights the importance of several previously overlooked features of attack and escape. In particular, we find that it is not the prey's instantaneous maximum centripetal acceleration but the prey's ability to sustain a high centripetal acceleration for an extended period of time that is the primary driver of the variation in catch success across species.