They are in conflict with each other, that's the problem. The US is only thrown in conveniently to muddy the water and as scarecrow but the aim is EU over member states in any case.
> the EU (as in all the EU member states)
No, it's the EU, not the member states independently as sovereign states. Note also that there is a huge difference between "European cooperation" and "EU integration".
Over time the EU has taken over significant levers of sovereignty away from member states. The single currency was a very big one (hence some countries decided to stay away). Now it is pushing into another very regalian domain, which is defence.
If there was a referendum in each EU country to ask the people clearly and honestly whether they were in favour of their country disappearing as sovereign state and becoming only a 'state' of a federal EU, my strong guess is that they would vote "no", but that's exactly what is happening little by little. That's my point, my problem with and fear about the EU (and of course the national governments that are in on it).
Quite disappointing to read the crass insults and accusations thrown by some commenters, as well as the barrage of downvotes. Unfortunately it seems to be an usual pattern (I'm getting uncomfortable 1984 vibes more and more).
The EU is the member states. The distinction is purely in your head.