It is really supposed to be a hybrid of the two. The primary focus was to have local governments that were most important to the lives of the citizens but that those local governments would be regulated by the federal government that was supposed to have the best interest of the people at mind with regard to freedom. Obviously, that concept was not well defended by the citizens of the US.
You, my brothers and sisters, were called to be free. But do not use your freedom to indulge the flesh; rather, serve one another humbly in love.For the entire law is fulfilled in keeping this one command: “Love your neighbor as yourself.”
The entire point of the constitution was that the states, like little children, wouldn't work together for the common good unless they were forced to by a guiding parent figure. The federal government was put in place by the constitution (and the articles of confederation were straight up repealed, so they are no longer valid at all) to keep self-centered state governments in check. It literally exists to tell the states what to do, because they proved they can't be trusted to do the right thing on their own.
And this isn't even getting into the issue of slavery.
The United States has been a single nation with sub-regions since 1787.
Liberté. Égalité. Fraternité.