Europe North-South is comparable to the US East-West coast distance.
Europe East-West is comparable to the US North-South.
The US has more land mass (and there is Alaska, which is the jolly joker card here - we can counterbalance this with the russian-speaking regions of the European continent, it is debatable whether they are "Europe" or not), let's say the lower 48 US is maybe two times the area of "classical" Europe. Europe is also much more densely populated.
So if you consider the USA to be the size of two postage stamps, then you might actually be correct :)
Area of Western Europe: depends on which definition you use. But smaller than Alaska by most.
"Europe is also much more densely populated."
Yes, it is. It is smaller and more densely populated, which means that rail transportation makes sense (note that you also see rail transportation in the more densely populated regions of the United States, such as the BosWash Corridor, Chicagoland, etc.)
Europe is the size of a postage stamp compared to the USA (or even worse, Canada).
Oregon is larger than the UK. Texas is larger than France. Alaska is larger than all of Western Europe.