As odd as this next statement will sound, I have an explanation for it.
Comparing the United States to Europe/the EU is really comparing apples to oranges.
What? Comparisons of similar countries are invalid? Why do I say these crazy things? Well, it has mostly to do with the origins of the countries.
European history is a much longer story than American history, and much of it is filled with monarchies arising during or immediately after the Dark Ages. With the feudal system so rigidly organized, it became accepted that governments had the final say in what happened, and the lowest classes (mostly serfs of the royalty) grouped together to exist as a commune rather than individuals. This helped them feed themselves more efficiently and allowed for some form of contact with equals, rather than constantly being ordered around by their many levels of social superiors. This mindset outlived the monarchies from which they formed and gave Europe the left-winged slant it has today. Quite often, the group is seen as more important than the individual, and that is reflected in the Socialist or pseudo-Socialist nature of most European governments. These governments have a long, powerful reach, and the general consensus of the populace is that they are the sheltering protectors. Trying to include an American-style limited government would leave people hopelessly wondering where their big brother went when it was such a big part of the country.
The United States, however, was formed by English malcontents, who were followed by malcontents from all countries of Europe, and eventually the world. These people saw their governments as power-hungry and dominating, and simply wanted to be left alone. They formed a new, limited government in the New World, and built a country around it. The mindset of the people was that their government should not have such an influence on the people, and they lived according to it. This is seen in the center-right nature of the American populace. Recent swings to the left notwithstanding, the US government is usually kept small(ish) and out of the way, at least comparatively. The American people prefer to sacrifice the safety of a powerful, protective government for the freedom to do most anything they like. The implementation of a European-style Socialist government would be met with outrage at best. The worst-case scenario is a military mutiny at the highest level. and a popular uprising from everywhere that is not the East Coast and southern California.
So Europe is more community- or group-oriented, and the United States is more individual-centric. Trying to compare the two comes down to a matter of personal preference. All other concerns are secondary to this.
Personally, I like the option of choosing my medical care, retirement plans, financial options, etc. But I can easily see how a state-run entity for any of these would be lucrative to some people.