I am not a lawyer nor a native english speaker, but in both cases we have a central power which limits the powers of the constituting states. In the USA you have the constitution, in Europe its the treaty of Lisbon. And there is a high European court which is the counterpart to the US supreme court. So I am not sure what the fundamental difference is you are referring to.
Both the EU and US structures of individual rights are based on philosophies of pre-existing, fundamental rights; both the EU and US have governing documents which establish legal rights grounded in those concepts of pre-existing, fundamental rights.