the states are autonomous in our system (much to the shagrin of the imperial fed folks), they grant power to the fed for certain things like national defense but they ultimately have the power to function as their own countries (see 10th amendment, or what's left of it). the eu is more like an over arching fed that rules everything.
in america, power and authority starts with the individual and works up. in europe it starts with the government (collective) and works down. that is why most europeans absolutely do not understand americans super strong sense of individuality and personal liberty even when it is against the collective. this is strictly my opinion, but i think it stems from the monarchical system of being "ruled". we just don't get that here and i think europeans and the rest of the world always want a certain aspect of that in their lives.