Quite a few differences, Sparta treated the women of their society as very important. They held their women on a very high importance and treated them as such. Spartans trained as warriors from birth were the rest of Greece did not view an army in that manner. There are quite a few other differences, but I'll just say that Spartan was a one of a kind society.

Spartans were warriers, trained from early childhood. They lived a life of minimalism and simplicity. Sparta was a monarchy. Athenians were more intellectuals and lived lives of opulence and beauty. Athens was also a democracy. Off course there are many other differences.

Sparta - it was a diarchy since it had two kings (agaid and eurypontid houses). but it also had the gerousia which was like an oligarchy (30 members including 2 kings), and the acclessia (dont quote me on spelling) which was like the rest of the spartiate men. they also enslaved fellow greeks. their slaves became known as the helots, a class above them were the perioeci (artisans) and finally the spartiates. while women had greater freedom, they were not allowed to vote, but did run other affairs in sparta. they trained in physcal activities, and often competed with the boys. boys from the age of 7 were taken away for the agoge, some later to the krytaeia (possible spelling) which would hunt rouge helots. Sparta was very austere with great emphasis on simplicity because of the great rhetra delivered by lycurgous. because of this they only had basic literary skills hence, most sources on sparta are from other greeks. spartiate males were expected to simply maintain physical fitness for war, and were part of syssitia (public messes). Athens - i dont know as much about athens, but i know they were a democracy with an elected leader i assume. their army wasnt really a professional one, as soldiers were conscripted, they didnt believe in enslaving greeks (although their activities in the delian league may be seen as oppressive). they placed far more emphasis on intellectual pursuits, hence so many philosophers, they also produced more art than spartans. women were hardly viewed as equals in athenian society. they tended to wear jewelery, perfumes to enhance beauty, spartan women were prohibited to wear such things. also athenian women were modest, had a more chaste image. spartan women appeared more sexually open due to their dress which often revealed their thighs in public. these two cities were total opposites, rarely have they ever agreed on much, both saw the other as threats to their system.