First, there seems to be some confusion about the interpretation of the links that The Calculus of Logic provided. All those rankings do not enter into the computation of the freedom index ranking, the last one of the list. So no, neither health care nor the items kniz mentions, do play a role in that ranking. [On preview, senorbeef, the comment no longer applies to your post].
How is the UN human freedom index computed? I found this link that explains that 40 indicators (the list is on the link) are assigned a 1/0 value, and then you rank the countries according the total number of points they got. In the ranking that appears in my link (from 1985, quite outdated), the US ranks 13th, with 33 out of 40. I could immediately identify only two indicators where the US would (today) get 0: “capital punishment”, and “right to homosexuality between consenting adults” [poor wording, in my opinion; at any rate, the existence of laws against homosexual practices in many states probably warrants a 0]. Also, the US doesn’t allow US citizens to travel to Cuba (and perhaps other countries) as tourists, so perhaps the “travel abroad” in 1985 also got a 0. US dopers might have an easier time trying to identify the other possible 0’s.
Leaving aside the UN assignments of 0’s and 1’s, which leaves no room for gray (for what is worth, I didn’t find a UN human freedom index for any year after 1991), the table of 40 indicators they propose seems to me a decent starting point for discussion.
My personal experience? I have lived for many years both in Western Europe and the US, and apart from the death penalty issue and higher taxes in Europe, I don’t recall major legal differences. Yes, some of the “vice” laws in the US (alcohol, gambling…) strike me as silly (at 18, you are responsible enough to drive a car, vote, legally own guns, but you are still three years away from being able to buy beer?), but admittedly those are minor quibbles.
On the other hand, a substantial difference I noticed is to which extent money is allowed to rule the political process. For instance, in Spain, and I imagine also in other European countries, during electoral campaigns, parties are given free advertisement time on TV, which gives a fighting chance to smaller political parties. Also, some forms of campaign financing in the US would be illegal in Spain. This was explained to me as a Freedom of Speech issue, but it leaves me with the impression that in US politics, freedom of speech comes with a price tag, to a larger extent that in other Western democracies.