Hamilton vs. Jefferson 

The conflict between Alexander Hamilton and Thomas Jefferson was a defining moment in American history, as the two men had very different visions for the future of the United States. Their differences were based on their backgrounds; Hamilton was born into an affluent family, while Jefferson hailed from more humble beginnings.

Hamilton favored a strong central government with power concentrated at the federal level, believing that this would ensure economic growth and stability. He also believed in creating a national bank to handle fiscal matters and issuing paper currency backed by gold or silver reserves. On the other hand, Jefferson preferred states' rights over those of the federal government and wanted to limit its powers whenever possible. He advocated for agrarianism rather than industrialization and felt that individual liberties should be held above all else when making decisions about public policy.

These conflicting views played out during Washington's first term as President when he appointed both men to his cabinet—Hamilton as Secretary of the Treasury and Jefferson as Secretary of State—in order to create balance within his administration. The resulting political rivalry caused tension between Federalists (those who supported stronger ties with Britain) and Democratic-Republicans (who sought closer relations with France). This ultimately led to America's "first party system," which shaped our modern two-party system today: Republicans represent conservative values like limited government intervention, while Democrats focus on liberal causes such as civil rights reform, social welfare programs, etc. 

Despite their opposing ideologies, both Hamilton and Jefferson are remembered fondly in U.S. history for their contributions towards establishing America's constitutional democracy we know today, proving that even though they disagreed strongly about politics at times, it did not stop them from working together successfully toward achieving common goals beneficial for all citizens, regardless of any ideological leanings one may have had then or now.