Try reading biographies of both men. That's the best place to start.
I'll tell you this for free, though: they hated each other. Jefferson disagreed with Hamilton on everything it was possible to disagree on.
Hamilton favored a strong central government. Jefferson preferred a weak central government.
Hamilton founded West Point Military Academy; Jefferson founded the University of Virginia.
Jefferson opposed the Bank of the United States; Hamilton supported it.
Jefferson came from a wealthy, noble family; Hamilton was the offspring of a poor clerk in the West Indies (some people even say he was part African-American).
The list goes on and on. They were polar opposites.