Is the mother superior to the father, taking into account Allah's saying: "But men have a degree over them"?

The verse mentioned in the question pertains to spouses and their rights, not to parents, and it indicates that the husband has a degree of right over his wife. As for who is superior between the parents, many scholars have stipulated that the mother is preferred over the father and takes precedence in dutifulness (birr), based on the hadith of Abu Hurairah, which states that the mother is the most deserving of good companionship three times, and then the father. This is attributed to the difficulties the mother endures during pregnancy, childbirth, and breastfeeding, as well as her shared role with the father in raising children.