Very different. The EU has a legal method of succession (article 50), the US was brought together under a strict constitution, creating a single federal government. Compared to the original Articles of Confederation:
> In dramatic contrast to Article VII–whose unanimity rule that no state can bind another confirms the sovereignty of each state prior to 1787 –Article V does not permit a single state convention to modify the federal Constitution for itself. Moreover, it makes clear that a state may be bound by a federal constitutional amendment even if that state votes against the amendment in a properly convened state convention. And this rule is flatly inconsistent with the idea that states remain sovereign after joining the Constitution, even if they were sovereign before joining it. Thus, ratification of the Constitution itself marked the moment when previously sovereign states gave up their sovereignty and legal independence
A better comparison would be the formation of Canada, or better yet: the Quebec referendum to separate from Canada (put to a vote of the people, but narrowly lost: https://en.wikipedia.org/wiki/Quebec_referendum,_1995)
> In dramatic contrast to Article VII–whose unanimity rule that no state can bind another confirms the sovereignty of each state prior to 1787 –Article V does not permit a single state convention to modify the federal Constitution for itself. Moreover, it makes clear that a state may be bound by a federal constitutional amendment even if that state votes against the amendment in a properly convened state convention. And this rule is flatly inconsistent with the idea that states remain sovereign after joining the Constitution, even if they were sovereign before joining it. Thus, ratification of the Constitution itself marked the moment when previously sovereign states gave up their sovereignty and legal independence