Marriage in ancient Egypt was considered a sacred bond though divorce was possible. Women and men had separate roles, with women running the household, which may have meant governing servants who would do the household tasks and child rearing. While marriages were arranged and required parental consent, love poems from the era abound, so love was in the air.
Marriage in Mesopotamia had characteristics of marriage in Victorian England. Once a marriage took place, the husband and father had full authority ofver wife and children and determined every aspect of their future happiness. The man could take a second wife or concubine and divorce was permitted.
Mesopotamian society was strictly patriarchal. There is some evidence that early Mesopotamian society was ruled by a council of elders comprised of men and women; but over time only men participated in government. Young men were usually trained in their father's trade, except for the sons of the nobility and the wealthy, who received some schooling. Girls stayed home and assisted their mothers with household chores until they married. Women did have some rights, in that they could own property in their own name and were entitled to divorce their husbands if they could offer sufficient grounds.
Egyptian family life was also patriarchal with the father responsible for providing for the household and the mother responsible for cooking, cleaning, etc. One important difference is that Egyptian society was matrilineal, that is one traced ones lineage through the mother. Mesopotamian society was patrilineal. The Pharaoh often referred to his wife as his "dear sister," which has led to speculation that royal marriages were incestuous. This is a matter of considerable debate.
No woman ever ruled Mesopotamia; but there was one female queen of Egypt, Hapshetsut. Interestingly, in portrayals of her, she is shown with a ceremonial beard, to appear masculine.
In some ways, the roles of marriage and family were similar to our current society. The Ancient Egyptians actually had a pretty advanced society in some ways. Women were even in positions of power, and when a woman is in power it is an advantage for all women.