When two people make two opposing theories it is often best to judge each based on their ability to predict, how it match current data sets, and how well it works out in experimental studies.
The incentive models, which take data from both biology and culture, claims a prediction that as you measure equality of opportunity and compare nations it will correlate to inverse gender segregation in the work force. The more equality of opportunity the higher gender segregation will be, caused by incentives that is derived from gender roles, sexual strategies, and sexual dimorphism.
The prejudices model make the opposite prediction. It claims that when measuring the equality of opportunity the higher it is the lower the gender segregation should be.
In order to resolve the question one measure equality of opportunity and gender segregation, creating data. This create a scientific valid argument in favor of one model over the other.
That is one aspect of the theory. An other aspect would be to measure difference in prejudices between different professions. If the model is correct then it should be able to predict based on such measure which professions are gender segregated and which are not, and inversely predict the level of prejudices exist per profession given any country. The incentive model claim that incentives are a large influence and such you could not make a predictive model based on measuring prejudices.
The incentive model also predict that nation where the incentives are different (based on Maslow's hierarchy of needs), you should see a correlated change in gender segregation. Incentives such as reproduction is listed last among the physiological need, so nations where water and food is scare for women should result in higher incentive to seek professions where those are easier achievable. The prejudices model would argue that there is no such correlation.
This is of course just a small sample in order to scientifically evaluate the two different theories. There is also matching philosophy theories (their names escape me right now), arguing in different direction to explain the data.