Thomas Jefferson was the main author of the Declaration of Independence, a US politician, and a staunch advocate of a small federal government. Jefferson felt that the US should have extremely strong state governments with a weak central government. This belief of Jefferson was rooted in his experience as an American colonist underneath the control of a tyrannical central government that implemented laws without the consent of the people. Jefferson would help to create the Anti-federalists.
Alexander Hamilton, on the other hand, was a veteran of the American Revolution and a strong believer in the need of a powerful central (aka federal) government. Hamilton felt that the federal government needed to have significant power over state governments, otherwise the US would develop into 13 different, unique states rather than a nation united by a common set of laws and beliefs.