The dollar amount of military spending isn't exactly the same as military strength, but they're certainly hardly uncorrelated. France, Germany, and the UK all have spending around $50 B, while Turkey's is only $13 B. So by that standard, the EU is way ahead of Turkey. And of course, with a larger economic base, is in a better position to ramp up military spending. On top of that, the EU has significant military exports, and AFAIK (which admittedly, isn't that far), Turkey imports a large portion of its military hardware. Taking a look at the Turkish Air Force, it seems to be primarily from the US and some EU, with domestic aircraft being mostly UAV. If this were to turn into a prolonged conflict, being reliant on your opponents for your hardware is an awkward position to be in.
But that's largely irrelevant. Europe and Turkey are all well within the US' sphere of influence. There's simply no way the US would sit by while EU countries and Turkey got into a full-fledged shooting war. This is almost like asking whether North Carolina would be able to defeat Maryland in a war; there's just no way there would be a war that involves just North Carolina and Maryland. Clausewitz said that war is politics by other means, and the EU and Turkey are simply too politically entangled for that "other means" to predominate. The only role their military forces will have will be forcing the confrontation on one's terms. Military strength won't resolve the issue.