The EU is rapidly moving in a federalizing direction (one of the reasons the UK left, which will probably accelerate that movement). The phrase "United States of Europe" is part of the vision behind the creation and evolution of the EU in the first place. By adapting a common currency and the Schengen area the EU members have already given up significant parts of their sovereignty. It's not as federalized as the United States is now, but it's certainly an oversimplification to claim that EU members are "fully sovereign states".
Furthermore, EU member states are, in terms of population, much closer to individual US states in size than any of them are to the US as a whole. My state has three times the population of Switzerland.
Furthermore, EU member states are, in terms of population, much closer to individual US states in size than any of them are to the US as a whole. My state has three times the population of Switzerland.