The European Union (EU) seems to presume that the mass production of European research papers indicates that Europe is a leading scientific power, and the so-called European paradox of strong science but weak technology is due to inefficiencies in the utilization of this top level European science by European industry. We fundamentally disagree, and will show that Europe lags far behind the USA in the production of important, highly cited research. We will show that there is a consistent weakening of European science as one ascends the citation scale, with the EU almost twice as effective in the production of minimal impact papers, while the USA is at least twice as effective in the production of very highly cited scientific papers, and garnering Nobel prizes. Only in the highly multinational, collaborative fields of Physics and Clinical Medicine does the EU seem to approach the USA in top scale impact.