Is what you mentioned regarding the non-preferability of men over women, and the interpretation of the Qur'anic verses (Men are in charge of women) and (But men have a degree over them), in addition to the issue of Eve's creation from Adam's rib, and the reward for men and women in the Hereafter, correct, or is what some shaykhs say correct?

Allah the Almighty has equated men and women in the essence of creation, honor, accountability, reckoning, and recompense. He has granted women rights and duties similar to those of men, while assigning men the degree of guardianship over women, not to demean them. The reason for this guardianship is that Allah has favored men over women with inherent characteristics (such as prophets, caliphs, and rulers, increased agnatic relation and share in inheritance, and the authority of divorce in their hands), and acquired characteristics (due to what they spend of their wealth, such as dowry and maintenance, and other expenses). The favoring of men here is a favoring of the male gender, not of every individual man over every individual woman.