This may cut both ways with regards to innovation. For example, Europe as come way longer than the US when it comes to automation in various sectors (see f.x. the recent Economist article about inefficiencies in the US retail sector).

The main US advantage wrt to the last generation of tech giants (i.e. Google, Facebook and Amazon) is language. You will reach scale far faster in the US than in Europe because you do not have to translate your product to new languages and markets. Thus the US giants reached scale before similar European products could compete.