Europe is not an ancient civilization. It is a continent and politically, an amalgamation.
Most of the "Western" civilizations old enough to attempt comparison with China were not European in the modern sense at all. The classic example is usually Rome, which treated most of Europe as barbarians to colonize and enslave. The engine and wealth of the empire was along the Mediterranean. Ancient Rome was thus really a Mediterranean power not a "European" one. I think you could successfully argue Romans had more in common with other ancient Mediterranean powers or even ancient Mesopotamians than modern Europeans.
As to the rest of your points true enough. It is well known that today's Europeans find themselves in between a rock and a hard place given the current split between American and Chinese hegemony.