The primary difference is the environment and problem solving.
A male protagonist is usually defined by his ability to IGNORE his environment. He is a man in spite of the world around him. No amount of hardship or bullshit is too much for the male protagonist. He doesn't need anyone else. He operates best alone.
A female protagonist is a product of the environment. Socialization is important. Her mental health is much more dependent on the people who raised her, who she grew up with, and what her history was. To know a female protagonist is to know her history. You need to know her parents, her siblings, who she was friends with, her first love, her first friend, how she was rewarded and how she was punished and what she was taught.
Another way to look at them by looking at how they would be antagonists. The Sorcerer and The Sorceress.
The truth is violence and the threat of violence has solved more conflicts than any other single action in the history of this world or any other. Because violence is so random, we hedge our bets and give that power to governments because as long as we all follow the rules, no matter how the rules screw us, we get to live if we play by them.
The sorcerer is a villain who seeks power so he can control the world by breaking the rules and returning to the most fundamental of truths, might makes right.
The sorceress is a villainess who seeks control so she can have power by using the rules we have established. Without society, the sorceress has no power and anything that threatens society is a threat to her.
A properly made female protagonist works WITHIN the system, playing by the rules, and winning because she can rally her allies to overcome her enemies. The male protagonist goes it alone to solve the problem, usually taking on the role of the DETERMINATOR. You can knock him down, but he will keep getting back up.
Whereas the female protagonist traps you by recording your words to use against you, by character assassination, by poisoning the well and turning allies against you.
Here:
www.scribblehub.com
Start there and read on, focusing on what's going through Lilith's head. She is a 'Villainess' in an Otome Game who is becoming slowly more self-aware of what she is and becoming "real". As you read about her, you will notice that everything she does is subtle as FUCK, but she also understands the results of her actions, the rippled across society because of her actions and the power of rumor. In the end, the MC could just walk up to her and murder her without a thought, but he is also at her mercy, if she decided to turn society against him.
The only reason society HASN'T turned entirely against the MC is because he has OTHER female allies who can play the game covering his ass.
But I think if you want to write a female protagonist, you focus on her history and make her a PRODUCT of how she was raised, where as a male MC is usually a rebel against his upbringing.
That, I feel, would be the primary element you should use if crafting a female protagonist. Everything else is just fluff. You can make her a tom boy, lesbian, fem fatal, wide eyed waif, battered and long suffering abused wife, perky adventuring princess, or whatever.
The Female MC is a result of her social environment FIRST, then everything else will be so much more believable.