Brawls no, not that I'm aware- though there are very opinionated fan-bases and supporters groups even state-side who have had great success protesting owners, abusive coaches, etc. In England the women's game was banned for fifty years so likewise, the fan base never developed the same way as the men's though that's changing.

I tend to watch big matches on the mens side so I will answer what I can. The physicality of women's matches here in the states is high, just check out I think Sierra Gordon on twitter a few days ago where she posted a rather, surprisingly, dirty blindside play by Alex Morgan. The women are scrappy, and play rough physically like they are in college still- whereas the men tend to hold themselves back more if you watch closely. The women tend to play every match of the league full throttle and that's because by the end of the season, you usually have four or five teams fighting for a playoff space.

Women foul more as their technique is generally worse, because of a lack of high level coaches in the youth side to engrain habits. That being said, they don't complain and fake like the men do. Some preppy youth players come in w that prep-school attitude as I like to call it, but in a season or three its usually out of them.

Tactically the game is slower, the game has more upper 90's goals, but a lot of that is lack of proper youth training too. Canada's womens soccer team had a female coach who drilled average passing speed as a team into them and they almost rivaled the mens statistics. I think that was 2011 or 2015 and they did v well. Do some research on that and you can probably find a whitepaper. Average passing per minute or something like that. Tactically too, a superstar or two still is capable of greatly influences the game at a high level, like basketball.