Individual European countries lacked the resources and manpower of either the USA or the Soviet Union. I mean, just compare them. France's population in 1960 was 46 million, and its GDP was $63 billion USD. The UK's was 52 million people, with a GDP of $72 billion USD. The US had 180 million people and a GDP of $543 billion USD. The USSR had +200 million people; it's GDP was maybe 50% of that of the US (so let's say ~$280 billion USD, I can't find an exact figure offhand), but they were willing and able to devote a high fraction of it to arms production. (I picked 1960 as a year that was significantly outside of the immediate postwar that those negative effects on their populations and economies would not be quite as profound, but you can pick other dates, too.)

So while many of these countries did have robust arms industries (the UK and France in particular, who even developed nuclear weapons at great cost, as "independent" nuclear deterrents), there is just no way they were going to develop something on par with either the US or the USSR. They didn't have the capability. Anything they did necessarily would have to be scaled down by a factor of 4 or so, even if they did spend the same percentage of their GDP on arms as the US and USSR did, which they didn't.

Western Europe as a whole had some impressive capability — this was went into NATO, for example. But it should be noted that the US found ways to strongly discourage too much military production in Europe: they were happy to have the Europeans be somewhat dependent on the US for military protection, and would prefer they purchased equipment from the US rather than build it indigenously. This "soft power" approach didn't always work (the French in particular were pretty independent and resented this kind of thing), but when there is a limited amount of money to go around, having a superpower essentially offer to take the burden of robust military spending off of your hands so that you could use that money elsewhere (many of these countries developed much better social safety nets, infrastructure, and other "expensive state things" than the US did and does)... it's compelling.