The difference between Hamilton and Jefferson was in their ideals and beliefs. Hamilton was a Federalist, and thus he wanted the state to have a strong, centralized federal government, where it would have most of the power. On the other hand, Jefferson, being a democrat republican, believed that the federal government should be weakened, and that the individual states should have more power - he wanted a decentralized type of a government. This feud led to the creation of two separate parties - the Federalists and the Democratic Republicans.