The two rival city-states of Athens and Sparta were both different in many ways.
One of the main differences was their form of government. Although both city-states had elected assemblies, Sparta was ruled by two kings while Athens was rules by annually-elected archons.
Spartan life focused around martial prowess and obedience. Slavery was put into place, which allowed young men to focus on military training. Young boys were training to be warriors while young women were trained to become mothers to warriors.
Athenians were much more creative. Education was the primary focus, which led to great achievements in both the arts and sciences. Military service was optional, and young women, while having more options than in Sparta, were stilled restricted in their freedoms.
They also had different ideas of the world around them. Sparta kept to itself, but did lend assistance when it was needed, such as during the Persian Wars. Athens wanted to become a major player in Greek politics, and tried creating vast alliances. The Deliean League was an alliance both military and trade which was the closest that Athens ever came to a unified Greece. This would eventually led to conflict between the two city-states.