I think your first observation is correct and I had similar concerns about Doug's otherwise brilliant observation. I think, however, that the underlying causes are structural, not just "prices" i.e. wages. One is self-employment - it is a wet dream of most toiling schmucks in the US, but its role in Europe most working class folk dream of good jobs rather than "being on their own." Since the self employed are by definition not unemployed - even though their work is economically marginal - its effect on unemployment rate is quite obvious.
Another element is what for the lack of better terminology can be called "marketisation of society." Many jobs in the US, especially in the service sector, perform function that elsewhere is performed by the so-called "primary social institutions" (i.e. extended family) or alternatively semi-public agencies taking advantage of the economies of scale. Child care is a good example - in Europe it is performed either by family (women who stay home because can afford it thanks to government subsidies to families with children or by grandparents) or by semi-public child care establishments (which are run more or less like schools). In the US, by contrast is the area of business venture and small often shadowy "fly-by-night" operations that nominally count as "employment" but basically involve women staying home.
Yet another structural difference is that the US economy seems to be particularly good at creating artificial transaction costs and turning them into business opportunities. Examples include: - health insurance involving a myriad of Byzantine private bureaucracies each employing an army of clerks (vis much simpler single payer systems), - regulation by litigation that creates business for an army of lawyers, - grossly inefficient car-based transportation system that creates business opportunity to an army of salesmen, insurance agents, and mechanics - inefficient housing (single family dwelling) that creates business bonanza for realtors and building contractors.
In other words US economy is able to create more jobs that benefit a few individuals but at the cost of gross inefficiency that harm most other people and society as a whole. So in that respect, US is somewhat similar to the Soviet Union where full employment was achieved by hiring people to perform unnecessary and meaningless tasks - the main difference is that the US is much better at building a Potemkin façade around it.
Wojtek