The main similarity between Athens and Sparta was their form of government, which featured an elected assembly whose members came from among the people; the primary difference between the two cities came from their way of life, as Spartan life was simple and ascetic, while Athenian life was more highly creative. Another difference involved the two cities' views about their proper relationship with the rest of the Greeks.
Athens and Sparta both featured an elected assembly, but Athens' executive leaders, the archons, were also elected from the people, while Sparta featured two kings that ruled until death, or until being forced out.
Spartan life focused on building obedience and preparing for war. From a young age, boys were taken from their homes and taught to grow up and be warriors, and girls learned how to be the mothers of warriors. The practice of slavery meant that the free young men could focus on military training while slaves ran the industrial and household duties.
Athenian life was much different, with many opportunities to receive a quality education and pursue studies in the arts and sciences. Service in the army or navy was voluntary rather than compulsory but was open only to young men.
Athens eventually developed a taste for conquest and tried to bring all Greece under its sway. This led to the Peloponnesian Wars, and the eventual defeat of the Athenian ambitions.