On the other hand...
One of the reasons that the US can offer better kit at a lower price is that, in addition to the domestic military market, the US can sell the kit to allies, increasing the economies of scale, and, incidentally, the profit margin. It's sort of like Microsoft deathware.
If the EU starts developing military hardware "at home", it will initially be pretty expensive. However, as the kit starts flowing through the R&D&Manufacturing pipeline, the incremental cost to develop a follow-on or new program will lower in cost, and economies of scale will start accruing to the EDA.
At the same time, the US will start losing customers for "excess" hardware, thus increasing the cost of US hardware, and, given the constant fight for budget over here, probably cause the cancellation of projects that would otherwise get funded because "we can always sell it to the Europeans".
The EU is as technically advanced as the US in nearly every aspect of technology and more advanced in many. While there are many "bits and bobs" of US technology in most EU military hardware, there are also "bits and pieces" of EU-developed technology in the US hardware as well. (Rolls-Royce engines and Siemens electronics to name two.)
So, as the EU develops its own military technology base, not only will the kit become more competative and start selling as an alternative to US hardware, but the knowledge an skills will grow to the point where the EU can supply more of the "bits and pieces" back to the US. And some of the "boondoggle" projects that get done in the US MIGHT get done BETTER in the EU...and sell back to the Yanks...
...who will start complaining about "all the good deathware comes from Europe"...
I'll get me hat and goat...