I'm not sure its proper to say that Athens was more "cultured" than Sparta; rather its culture was entirely different. Athens was a democracy ruled by a council of the citizenry. All major decisions were made by the council. Sparta was surrounded by hostile people known as the Messenae, who never missed an opportunity to rebel. As a result, the Spartans of necessity remained constantly ready for war. It was not so much a matter of their being warlike by preference as that they had no choice. Both spoke the same language and worshipped the same Gods, although Athens tended to venerate Athena, its presumed founder, and Hermes, the messenger of the Gods. Sparta, as one might expect, venerated Ares, the god of war.
Both societies had growing populations and established colonies throughout the Mediterranean. Both on occasion forced city-states throughout the Peleponnese to ally with them. This competition for Allies led to the Peleponnesian War which ultimately resulted in the destruction of Athens.