Answer: The Democratic Republican Party and the Federalists
The Federalists wanted a strong federal government whereas the DRP defended states' rights.
They disagreed on central banking, Hamilton(Federalist) wanted to have a federal entity to control the issuing of money(a central bank) which Jefferson(DRP) strongly opposed since the power of the bankers to control monetary creation would endanger individual liberties.
They disagreed on their interpretation of the Constitution, someone like Marshall (Chief Justice of the USA, 1800-1835) defended a loose interpretation of the Constitution whereas Jefferson stood for a strict interpretation of the Constitution.
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