That's not entirely true, Airbus is a participant in most European military aircraft projects. They participated in Eurofighter for example and are part of the FCAS program.

It's true to the extent that the US does a lot more and broader military procurement in general, so Boeing gets a smaller piece of a much bigger pie. Wheras Airbus is getting a piece of most European projects as a member of one consortium or another, it's just a smaller pie.

Are they? Airbus has its hands in quite a few major military programs (Eurofighter, A-400M, Tigre, Super-Puma, ...), as well as in spatial programs, especially satellite intelligence.

compare to Boeing's volume? maybe, but Airbus is one of _Europe_'s largest defense contractors