How did the rights and privileges of women differ within Greece between Athens and Sparta?
In general, women in Sparta were somewhat more free than those in Athens. Women in Athens were fairly closely regulated by their husbands. It was thought that their place was in the home and that they shouldn't even go out in public much. Any time they went out in public, they were supposed to be escorted by a man. Their main purpose was to have children and run the household.
Spartan women had more freedom. Their husbands lived in barracks rather than with them. If they had sons, they left their mother's home at age 7 to live in barracks. Spartan women had slaves to work for them and their time was supposed to be spent more in getting physically fit. They were supposed to train just as hard as the men so that it would be easy for them to go through pregnancy and give birth.
In addition to that, Spartan women could inherit and own property from their families and husbands. They held a lot of power because the men were often away at war.