A similarity is that they both wanted some type of Republic, while they also believed they were doing the best for their nation. I predict that the future conflict between the North and South will have to do with with wanting to expand their land.
One difference is that the Federalist Party wanted to create stronger ties with the British while the Democratic-Republicans wanted to create stronger ties with the French. The Democratic-Republicans wanted to provide more economic support for the working class (South) and the Federalists wanted to provide more economic support for industry and manufacturing (North).