Men and women are not two completely different species needing a completely different diet, and the basis of what food and nutrients we do need is a little more personalised than gender alone.
The biggest factor we need to consider when answering this question, is what are you doing? What training are you undertaking and what are your end goals? If, for example, a male and female of similar size and weight are both strength training with similar goals in mind, their protein intake wouldn’t vary all that wildly. If, however, you’re working towards a very specific goal, then both your diet and training needs to be smartly planned based on your indivdual needs, and consulting with a professional is always recommended.
In terms of a general daily protein requirement, there are some guidelines available. If you want to know more about protein's role in our diets, check out Dr. Nick's blogpost, here, and below is an overview of how much protein you'll likely require:
If you train regularly you should be aiming for 1-2g of protein per kg of body weight. That’s a wide range, which needs to be adjusted depending on the type of exercise, the intensity, and the frequency. If you don’t train, this could be closer to 0.8-1g per kg.
For example: A 75kg man, training regularly would require 1.6g/kg of protein per day. So, 75(kg) x 1.6(g/kg) = 120 grams of protein a day
Of course, it's important to note there's no ‘one size fits all’ and everybody is different, but thinking about your training and diet in tandem, will bring you the best results.