France and Spain have population densities similar to the Eastern US - 220 people per sq. mile.
The idea that Europe doesn't have a well developed personal auto system is silly. I guess you've never driven in Europe on the Autobahn, Autostrada, etc.? Its just like in the US, except their roads are in way better shape and far better designed, and you can drive much faster, and half the drivers are in what we would call high end/luxury models (Mercedes, BMW, Porsche, Alfa Romeo, Volvo).
Distances between European cities are not "short" unless you are thinking of just going around the Netherlands or Belgium. Medium distance? Maybe. Paris - Frankfurt or Cologne - Munich or Milan to Rome = 360 miles. About the same as Cleveland to Chicago or New York to Richmond or San Diego to San Francisco. Madrid to Berlin is 1500 miles - sames as New York to Dallas! Europe is actually really big - in fact, bigger than the US with Alaska and Hawaii - 3.8 million square miles. That's only slightly smaller than the size of the lower 48 states (CONUS) + the 100 mile strip of Canada where 95% of Canadians live + all of Mexico. Population of Europe is about 700 million. Population of US + Mexico + 100 mile strip of Canada is 500 million.
I hope the Cato Institute had its facts together a little better than you!
In another article, "Yet the metropolitan population density of the United States is still about one-fourth that of Germany. New York, our densest city, has approximately one-third the number of inhabitants per square mile as Frankfurt." "One third of EU citizens live in cities of over a million people, rising to 80% living in urban areas generally." Compact cities in densly populated countries.
All of the EU is only 1.7 million sq mi, less than a quarter of the US. Europe is much smaller than you think. It's far from Madrid to Berlin, about 1100 miles, but about 30% shorter than you say. If you wish to start including the non-high-speed rail areas of Eastern Europe to the Urals and through to Turkey in your comparison, let me know.
While Europe has some very good highways, only a few people travel on them, and those people don't travel very far. I'll get back to you an the total miles by rail and road/ person /year in both areas later.