The key principle to understand in contrasting the two cultures is that Sparta was a warrior nation built on a warrior nationalism and Athens was based on intellectualism.
Athenians did much to advance basic cultural dimensions (art, math, government, commerce, philosophy) that would become foundation material for the the most powerful culture in the world - Roman Empire.
Sparta did much to advance the right of individuals and equality but primary through military services.
Spartans society was based on minimalism in all things. (Look up the word spartan in the modern dictionary). Equality was a core element of their society.
Athenians were maximists. They believed in social classes and that fundamentally some people (ruling class) are absolutely better than others (working class).
Their combined influences led to the principle that the individual's rights are important. It is a collection of individuals that empowers a government to rule over them.
Western Civilization has the Romans to thank for absorbing and integrating both of these cultures and several others into the Roman Empire. As Roman conquered the whole of Europe, parts of African and Asia, these ideas were transplanted to the local societies where they took root.
If you needed to be in a fight, bring a Spartan with you. If you needed to win a debate, bring an Athenian.