Hamilton v. Madison 5

Obviously the debate did take place in writing, but it would be a great opportunity to see the fundamental debate of federalism in person, with direct point and counterpoint. Plus, they could both clear up some ambiguities in the Federalist Papers.

Hamilton of course believed in a more expansive central government more directly involved in economic affairs, not necessarily in the modern regulatory sense, but in terms of a central bank (which was proposed at the time, and opposed by Madison), money for the arts and sciences, etc. Madison was more of a government governing least persuasion, who essentially opposed the industrialization of the economy, politics, and culture of the country favoring agrarian virtue. Hamilton had his eyes set on the future, and was one of the early proponents of "corporate personhood," a debating starting to rage today.

It would be a gross oversimplification to argue that Madison represents modern conservatism and Hamilton modern liberalism. There are incongruities on both counts.