The major dividing factor between the Federalists and Democratic-Republicans was how much power the federal government should possess.
The Federalists believed in a strong federal government. This party argued that America already experienced a weak federal government under the Articles of Confederation and the results were awful. This constitution lasted roughly a decade and allowed chaos to ensue.
The Democratic-Republicans argued that there should be a federal government with less power. This party felt that state governments have a better idea of what laws/customs will benefit their citizens. Along with this, the Democratic-Republicans were worried about the federal government gaining too much power. This fear was rooted in America's experience as British colonists.