One thing I think would be different is in the direction that the government/people look. My impression of Beta from the books is to still be forward striving and looking while being proud of the past. Switzerland reveres the past even as it moves towards the future, cautiously, slowly. It took invasion by Napoleon and a later civil war to cause a central government to be permanently established.

My impression of Beta is that they are more fractious a political economy with quite the vigorous system of voting. And their mania for voting would reflect the American ideal where early in history we did things like voting on the leadership of military units or which way expeditions should go. It seems very much like how the Lewis and Clark expedition decided what to do in some instances with everyone, including the black slave and the Indian woman, getting a vote.