There's still Federal taxes which get paid, and distributed out to the states. Whereas there is no "EU" tax that gets distributed to the member states.
EU levies "EU taxes" to its member countries and then distributes part of the money back. It doesn't collect these taxes directly from EU citizens, but that doesn't mean the tax incidence wouldn't be on citizens.
EU collects about 0.3 % of VAT revenue of each country, and about 0.7 % of GDB of each country as a membership fee (which is the largest source of income).
EU also keeps most of the import duties levied on non-EU products.
