And from a purely European perspective it looks like the US is trying to do the same. We just don't have the full picture of either side.

Europe did not push enough in the software market, which is where the US is definitely on top. There's tons of specialized engineering companies in Europe that manufacture equipment that can't be done anywhere else. Less public coverage because it's not consumer facing, but ASML is just one example of it (who are well known publicly of course). There are obvious factors right now (e.g. war in Ukraine) that put a strain on public spending, but that's also the case for the US, and before that covid, and honestly when's the last time this has not been the case for everyone. Though the EU currently also needs to first scramble to reduce it's dependencies (especially in energy).