Perhaps women just aren't as vocal about their opinions?

I don't think collaboration and fighting are as opposite as your title makes them seem. If you have the problem/fight out in the open, it's a situation that can be developed and improved. If people disagree but still 'collaborate' no progress happens and frustration accumulates. If I were a consultant I'd sell this to you as fighting being the best form of collaboration.

In fact, I'm following negotiations within an international project, where there is a power fight going on due to personnel changes. Formally everyone is collaborative and open, but under the table the fight is dirty and vicious.

I think it would be better to say openly how you feel and what you want - instead of acting polite and using excuses to undermine the other partners' suggestions. Is this what "being civil" means?