Put simply, Athens was the brain, Sparta was the brawn. Sparta was the "military superpower" of Ancient Greece, even their women were very skilled at combat, Athens, named after Athena, goddess of wisdom, was all about art and science and literature etc. which not only cause feuds between the polis' but drove their success. Also, Athens relied on trade to get what they needed, while Sparta relied on farming and conquering other lands.
