What were the main disagreements between the Federalists (Hamiltonians) and the Jeffersonian-Republicans in the early years of the nation? Why were they so divided?

There was a lot of disagreement in the years following the American Revolution between the Federalists (Hamiltonians) and the anti-Federalists (or Jeffersonian-Republicans). Conflict arose in the wake of the Revolution, when the first attempt at forming a new government proved a failure. Hamilton argued in favor of a large central government, one that included a national bank. Hamilton envisioned a government strong enough to manage the development of an industrialized national and global superpower.
Anti-Federalists, on the other hand, argued in favor of a small federal government. Remembering the abuses of King George III, Jefferson was very much against giving power (and tax money) to a large, remote government that didn't understand, or care about, the needs of the individual citizen. Jefferson envisioned a nation of yeoman farmers, where every family could be a royal family on their own plot of land. He imagined a rural, agrarian population liberated from the constraints of an overbearing government.