I accept that Eve by listening to the Serpent brought us into sin and Mary by listening to an Angel bore our Savior. That was the women's part in this life. She can either be like Mary or be like Eve. I being a Catholic choose Mary to copy.
As for each individual person they have vices and virtues. They are suppose to conquer their faults and cultivate their virtues.
Having a competition about who bore the greater fault solves nothing. It just gives the other gender bragging rights.
Women are either the greatest detriment or greatest help to mankind, in extreme examples, as in Eve and Mary. Mary would never exist without Jesus' sanctifying grace, it's said that before Mary was born Jesus already cleaned her of her sin through dying on the cross. It's great to meditate on. Point being, through man women are saved, 1 Timothy 2 15. Eve bore no children before the fall, therefore had no occupancy, had a plain woman's heart, and in that sense the fall of man was made to happen. In many cases the Bible states the man makes the vow of union to the woman, not the other way around. Even though she wants to originally, woman's vow holds little weight and she must prove herself through childbearing. Other obligations, if not children. Once woman had children, and everything is handled by God, she has by then proven herself, therefore the woman bearing life [from a virginal state] is the vow of fidelity to the man.
When man fell, Eve bore son of man, and of God. If we as men choose women who are sanctified from their fall, penitent virginal spouses, we may be fruitful and multiply within the graces of the Church, therefore God, therefore only have capacity to generate children of God directly. A man makes a vow because man has proclivity to be adulterous, polygamous as some may say, and if he falls he is breaking the covenant between himself and God. Leading to broken homes etc. Therefore, the man's strength & responsibility, and woman's stewardship & obedience, makes the greatest bond known to man, and has caused not the fall, but the redeem of man. Everything in it's correct order, which man has to grasp ahold of through God before continuing to have children in the proper sense. Women have no say in this, 1st Timothy 2 11-14. Lucky for her, all she must do is submit, as every Saintly woman has done. Maybe one or two have had the vocal proclivity of a man, in over 6000 years. Foolish women attempt to replicate those Saints.