If the ECJ rules something, the EU Member State must abide by that ruling, even if a more local court has already ruled differently? If so, then the ECJ is a superior court. If there is no court above which can be petitioned to hear the matter, they they are the supreme court.
I totally follow your line of thinking, I just slightly disagree. The EU is a not a country. It is a group of countries which have a bunch of treaties together, making them close friends. The ECJ hears and rules on disagreements between countries.
The ECHR only rules based on the ECHR, and can only marginally touch the "local" member states' parliaments decisions (local laws) and practices.
The SCOTUS is the highest legal authority for a federation. If you'd like a EU comparison: Germany is a federation. The SCOTUS makes decisions based on the US constitution, not on a bunch of treaties between member states.
Now of course, you can go back and say "that's not what I intended to say", but in that case I'd like to refer you to the original message I was responding to which said:
and my simple response was "there is no such thing as the EU supreme court". And I'll happily stand by that. No single court has been appointed the Supreme Court of the European Union, with jurisdiction of every legal matter in the EU. SCOTUS does have jurisdiction over pretty much every legal matter in the US. And that is what I pointed out.