.eu domain usage isn't that high, I don't think. I only have anecdata from my time in the UK, but .co.uk appears to be "the" domain to have in the UK.
From what I've seen the same is true on the continent. .fr and .de for example are highly popular in France and Germany. You rarely see local business reaching for .eu domains.
According to wikipedia, the number of affected domains is 344,584. Also compared to wiki there are 11M .uk domains and 16.5M .de domains. According to EurID[0] there are 3.7M .eu domains