Both of these visions of what the United States should be can be rationalized and seen as logical and appropriate visions.
The Republican vision (please note that these people are also called “Democratic-Republicans” and are not the same thing as the modern Republican Party) can be seen as rational because it sought to preserve and enhance traditional ways of life. The Republicans had a vision of a very traditional America in which essentially all people were small farmers and the state governments were much stronger than the national government. This would be a country in which everyone was equal because they were all doing the same kind of work and because everyone would be their own boss. It is rational to want to preserve what you have and to want to have as much control over your own life as possible.
The Federalist vision was also rational because it understood the need for change. A country cannot grow if it tries to remain the way it always was. The Federalists wanted a country that would allow industry to grow and that would be bigger and more united. Without their vision, the US would not be a world power (or even a rich nation, comparatively speaking) today.
Both visions were rational and both visions continue to have some applicability today.