While undertaking a study of Mesopotamia vs ancient Egypt, we need to know that both were great civilizations and contributed to the development and culture elsewhere in the world. Both were exposed to different geography and had to bear the brunt of foreign invasions as well. There was much influence from outside from invasions which also helped shape diverse beliefs.
Ancient Egypt was always characterized by strong authority concentrated at the center whereas Mesopotamia saw politics divided along regional lines on the basis of several city states. Egyptian monuments were gigantic in nature compared to those in Mesopotamia where the accent was more on literary elements. The cultural diversity between Egypt and Mesopotamia had much to do with the geographical differences.
Egyptians used large stones for their monuments as they were easily accessible and there was a large pool of laborers to build the gigantic structures over a long period of time. Egyptians were obsessed with afterlife which necessitated the building of tombs and monuments, a trait not common among Mesopotamians. Mesopotamians were not into preservation of the dead like Egyptians which explains the prevalence of pharaohs.
Women, commerce, art and culture:
Trade was extensive, but when you compare commerce in Mesopotamia vs ancient Egypt, the former was more advanced technologically. Mesopotamian geography helped in shaping and implementation of thoughts faster than the Egyptians who had difficulty in managing the environment along the Nile valley. Commercial law and the merchant classes gained more prominence in Mesopotamia.
But the status of women was higher in ancient Egypt compared to Mesopotamia where it declined after the Sumerians. The reason was that there were a large number of goddesses in Egyptian religion and womanhood was considered the epicenter of creativity. Compared to Mesopotamians, ancient Egyptians were far more colorful and lively in the portrayal of art and culture which remained unaffected by warfare and invasion.
Social differences existed in both places with the priests and nobility being at the top of the ladder. Both the civilizations in their own way left an imprint in the region and the adjacent places as well.