The US is a nation state, the European Union is not. Comparing the two should only be done with a truckload of caveats to begin with. If anything, compare the Eurozone to the US.
>>standa+(OP)
With visa-free travel, common regulations, etc., the European Union is certainly starting to approach the United States (notice the plural in "States"?) in developing a similar federal structure.
>>ummonk+d1
Brexit shows that there's still a major difference: member states can elect to leave. Economic penalties etc follow, and political fallout, but here in the US we fought a major war to demonstrate that states are _not_ allowed to secede from the union. (As much as many blue states might wish they could ...)