I always think of Athenians as lovers and Spartans as fighters. It's a gross overgeneralization, but a fun one. Basically, Athenians had a more open and artistic society, and valued cultural efforts. Spartans, on the other hand, valued physical strength and war.
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.
In truth, it is difficult to identify many similarities between the two cultures. Athenian society placed great emphasis upon education, participation in exchange of ideas, and the direct democratic form of government that developed there. Athens provided opportunities to engage in theater, art, sports. In contrast, Spartan culture focussed almost completely upon the development of the military training of those who would become its warriors.
The major difference was that the Athenians were more "cultured" whereas the Spartans were more of a warrior society. This can be seen even in their political affairs. The Athenians had a democracy whereas the Spartans had a monarchy. In general, the Athenians were a lot more interested in having what you might call a well-rounded society with lots of the good things in life. The Spartans, by contrast, were focused mainly on preparing themselves to be good at war.