Actually, the taxes per capita are about the same in the US and Germany. In fact, they're about the same in all of the major western countries. (Canada is actually a bit behind the US.) Average tax rates are lower in the US, but that's because the US has higher GDP per capita.
Therefore,if Germans get better services, it isn't from more tax money. Given that, it's absurd to think that US public services would improve given more money....
No - defence doesn't explain the difference.