That's not necessarily true; as the EU had many major players, especially historically: SUSE, Ericsson, Nokia, SAP; all were or are being shredded by US competition despite a domestically entrenched position. Even in 2008, when both economies did badly, the EU and the US had nearly identical GDP figures.

The EU might point to ASML as a point of pride; but that assumes an ASML competitor wouldn't get tens of billions to compete the moment ASML is inconvenient.