Federalist were in principle of the view of a limited republic, therefore their interpretation of the Constitution was more or less a set of principles to ensure the supremacy of the upper classes and of the whites against non-whites. Summarizing, they were conservatives, with the view of establishing a strong national government, and internationally more sympathetic to Great Britain than to revolutionary France, and then to Napoleon. Famous constituents were Alexander Hamilton, John Adams, and John Marshall. Geographically they represented the elites of the cities (such as Boston, New York) and New England. Due to their view of a more centralized government, economically they appealed to the creation of a national bank, the creation of a national debt.
In contrast, Democratic-Republicans opposed this views of a strong centralized government, view it as a potential threat to republicanism, were Francophiles (although moderating it specially after the Reign of Terror) and strongly opposed the idea of a National Bank. Constituents were Thomas Jefferson and James Madison. Geographically they rerpesented the South, and the frointier.
Explanation:
The creation of the parties reflected the contradictions of the independence war, and of the previous Continental Congress. Broadly, it was the sense of the continuation of a British-style of government, with a strong centralized federal state, and in a way pro-oligarquic (not a democracy) much as British parliamentarism had been working since the XVII century, this were the Federalist, and its geographical base and constituents reflected this, for example Hamilton was a New Yorker lawyer, advocating for manufacture and trade, with a strong professional army, or John Adams who hailed from Massachussets and was also more sympathetic to a commercial economy and of normalizing the US-Great Britain relations (he was indeed appointed as ambassador to the British court).
In contrast Jefferson and Madison shared the view of a democracy based on small agrarian property, did not favored a strong centralized government and also supported Francophile views (although always from the point of view of keeping the US neutrality). The geographical base reflected this, as the South was a collecton of latifundia, while the frontier, ever-expanding was the terrain of dipsute for the landless.
Thus the Democratic-Republicans were innovative in the political, but conservative in the economics, while the Federalists where conservative in the political and innovative in economics.
