IANAL, so happy to be corrected, but my understanding is that EU and US law work in quite different ways. EU law sets general rules, and law courts decide what that means with reference to existing legal precendents. US law is very, very specific about what each clause means and how it should be interpreted.
Every time I see these kinds of discussions I wonder if quite a few of the disagreements are due to e.g. US commenters worried by the relative lack of specific details.
Citing: Civil law is a legal system originating in mainland Europe and adopted in much of the world. The civil law system is intellectualized within the framework of Roman law, and with core principles codified into a referable system, which serves as the primary source of law. The civil law system is often contrasted with the common law system, which originated in medieval England, whose intellectual framework historically came from uncodified judge-made case law, and gives precedential authority to prior court decisions.
The US has federal law that apply to all the states. The EU has binding resolutions (the general rules you mentioned), and then each nation passes its own implementation. It's similar to the US federal RealID act which set standards for licenses that the states could implement however they wanted.
Every time I see these kinds of discussions I wonder if quite a few of the disagreements are due to e.g. US commenters worried by the relative lack of specific details.