Jefferson was a Democratic-Republican and Hamilton was a Federalist.
In the early days of the republic, there were two political parties that were different from the ones we know today. Jefferson was the leader of one, and Hamilton was the standard-bearer for the other.
Jefferson, a Democratic-Republican, favored:
- A capital in the south over one in Philadelphia
- Trade and foreign relations with France over Great Britain
- The interests of southern planters and slave owners
Hamilton, a Federalist, favored:
- A central bank and Federal Reserve
- Severing ties with the French Revolutionaries and strengthening relation with England
- Northern business interests over southern planters
Each man was more progressive in some regards and more conservative in others than the other; there is no precise correlation between the parties of the late 18th Century and those of the modern era. And they compromised with one another over having a central bank and a capital in the south.