The US isn't as huge as you seem to believe (or Europe not as small). Europe is not as square, so its land area is much smaller, but the distances are comparable.
A trip from Hamburg to Vienna is not that much shorter than a trip from NYC to Chicago, but it's easily done by train in Europe: Board the NJ491 at 8pm in Hamburg central station (in the city centre, no need to be there more than a few minutes before boarding), have a good nights sleep, get your breakfast served at your bed (in the comfort category), take a shower and arrive well rested in Vienna (city center, no need to wait for your luggage) at 10am the next day.
Admittedly, a lot of people do fly from Hamburg to Vienna as well, as it can be cheaper than the train due to tax exemptions for the airlines (not everything is perfect in Europe), or they just don't like sleeping in a train, but these trains are usually well utilised.
EDIT: The link to truesize doesn't seem to work correctly, here's what I meant to show: 