Is there a real difference between Thatcher and Reagan? Hillary Clinton and Bill Clinton? I can't see one. Generally speaking, female politicians are fairly similar to male politicians.
Ideally, we'd have a much wider variety of people in general serving in politics, leading to a better spread of opinions and perspectives. In that situation, without misogynist biases in the background, I suspect we'd see that female politicians are slightly more likely to be collaborative and male politicians are slightly more likely to be competitive. Both approaches are good and need to be in any room.