Athens was well known for its advanced educational system in which boys were trained in(drama, lit., philosophy, etc) which girls did not get. They gave birth to what is known as the "classical style". Athens was also the center of advanced medicine and science. Athens was the birthplace of the political democracy.
Sparta was a brutal, illiterate, unenlightened civilization according to Athenians and was more propaganda than truth. While the Spartans are mostly remembered for heroism on the battlefield, this is a very narrowminded view of them and their legacy. Sparta was more important to warfare because of its innovative diplomatic techniques and military strategies.