European companies are smaller on average and less likely to go public in general, so market cap comparisons don’t show the whole picture. Growing big is less often seen as a goal than in the US. “Megacaps” aren’t necessarily considered a healthy thing to have.
I don't see any sense in which the EU has fewer capabilities. It has, say, a smaller number of businesses with smaller market dominance.
It isnt clear to me what capability the EU would gain by having a monopolist social network, a monopolist search engine, a monopolist advertising trader