On the whole - man or woman - there are submissive types who just don't enjoy jousting with others and there are dominant types who do. I think it has more to do with one's native personality than one's sex. What comes natural to a person comes without effort, and if being dominant or domineering comes natural then you can tirelessly do it over and over while the others around you get worn out with it and eventually submit to it. This is the general human dynamic I have observed in people. There's some overlap there between this idea and the natural tendencies of men and women. Men having more confidence for example - for which T can be largely responsible - women being more subject to changes of mood due to E and so on, or being stereotypically nitpicky about things. You can see where confidence aids in being dominant, or where being nitpicky could win over in a situation just by sheer repetition... and if these things come without effort (i.e. are hormonal) then they can be done ad nauseam and often unconsciously.
But, to stress, I think the major part of a person's dominance or submission comes from their own natural personality. I consider myself of the more dominant variety, although I'm not interested in posturing to other people. I'm only interested in having full control over anything I do and my own life and in that I am absolutely dominant. I don't get off on telling others what to do. But some people do, male and female. And then there are other people who just want a quiet life, male and female, and who sometimes become doormats to other people because of it. A well-balanced person will exercise dominance where sensible and productive and not constantly dominate or constantly submit.
I would hesitate to say that women are "submissive" because I am descended from several that like to dominate, and the women in the family typically get their way due to a combination of assertiveness and selfishness. But at the same time with these women, that only seems to work if others around them don't stand up to it. If they do, then I've seen those women suddenly claim to be the victims in the situation... and they are believed. So I'm not sure - I would say women can use submission as a weapon too when dominance doesn't work, in which case it's not really "submission".
But on the whole most women don't seem to like violence or being in the middle of it, or being macho. They're often no less domineering, they just have a different method of going about it. I suppose you would call it "soft power" but power nonetheless.