Men Act, Women Are - Male badasses go out and beat up the enemy...female "badasses" sometimes do, but are often Chickified so the men can act and be awesome. Women can still get sympathy just by being women, or providing Fan Service, which leads to...
Men Are Strong, Women Are Pretty - Male badasses are clothed and in Western media, often buff or scarred or something emphasizing "masculinity". Female badasses are barely clothed and often are like supermodels. Even fighting styles are different: Men often have plausible (or semi-plausible styles)...women often have She Fu.
Men Are Generic, Women Are Special - Male badasses can be scarred, be a victim of Gorn or even die, and they'll probably die more often, but they at least usually get Heroic Sacrifices. Female badasses are not usually scarred, rarely victims of Gorn, and they don't die as often unless it is to motivate a male character.
Men Use Violence, Women Use Communication - Male badasses use tons of violence, female badasses can too, hence Action Girl, but honestly...how many scenarios can you think of where the man is passive and tries to sort out the problem without violence while the woman charges into a fight guns blazing? Other than Black Lagoon, there aren't many series where this is common.
Never a Self-Made Woman - Especially if she's the main character, an Action Girl's relationships with her (actual or surrogate) family will be an important part of her character (Xena and Gabrielle, Buffy and the Scoobies, etc.). Jennifer K. Stuller's Ink-Stained Amazons and Cinematic Warriors: Superwomen in Modern Mythology contains some detailed analysis of this.
- This troper is familiar enough with gender dynamics to posit that some of these gender issues are, in part, from the female demographic rather than the males. Ultimately, women and men have distinct biological niches regardless of legality, regulation, or medication (though surgery is a valid 'remedy'). Those facets where women hold a monopoly (i.e. motherhood) or genetic imperative (physical attractiveness/health) are exclusive points for weighing a woman as a woman (rather than as a person in general). Those facets where a man typically holds a biological advantage (physical strength) or a biological imperative (i.e. accumulation of wealth) are areas where Action Girls and related tropes tend to tread. When a girl or woman treads on a man's territory, she's an Action Girl. Keep in mind, "Guy Stuff" generally includes risky behavior or such activities that place the man as 'disposable.' Only those action roles falling on archetypal female ground (i.e. The Matriarch/Mother) and non-disposability will generally see an Action Girl measured as a woman.
- Changes in gender dynamics produce all the varieties of Action Girl and Faux Action Girl you can think of. There are no real-life biological imperatives for women to strive for attractiveness or for men to strive for wealth, but there are certainly cultural imperatives for both. (Plenty of people argue otherwise, in the same way anthropologists often fall into the trap of thinking marriage is the same across every culture, thanks to ethnocentrism.) That doesn't mean the imperatives don't exist, though; thanks to Your Mind Makes It Real, plenty of people in Real Life either are that way or write characters that way (it's always easier that way, after all). More Action Girls are likely to show up in fiction as these cultural imperatives slowly dissolve and transform. Of course, you'll also get backlashes with portrayals of female characters following more traditional gender roles, as men and women who are used to The Way Things Are try to keep things that way. Status Quo Is God, after all, until it isn't anymore.