I work for a European company here in the US.  The benefits your friend mentions are certainly nice for those who are able to get jobs in the first place, but ultimately they function in the same way as an increase in the minimum wage.  They simply raise the cost of each employee, which means that businesses can afford to hire fewer of them.  It also means that each prospective employee must be that much more productive in order to secure the relatively fewer positions that are available.  This harms the least productive members of society - the ones who, for whatever reason (language barriers, education, inexperience, etc.) haven't yet developed the skills necessary to obtain the kinds of jobs that deliver the benefits your friend has in mind.  The greater benefits do not act as a floor that lifts everyone up - they act as a hurdle that anyone who wants a job must jump over.  The higher the hurdle, the fewer people there are who are capable of clearing it.  That's one reason why many of the European countries have such persistent high rates of unemployment, putting a further burden on the remainder of the population to fund the welfare state through taxation.

That being said, it seems the US government is doing everything it can to raise the cost of employing people here as well, albeit in different areas.  Only time will tell if our current rate of unemployment ossifies and becomes a permanent fixture of American life.

So what about Denmark?  They have the highest taxes, very generous employee benefits, very generous social programs, has very low unemployment, and it is relatively easy to start a business.  They generally rank as one of the happiest nations in the world, crime is low, poverty is low, the society is very democratic, and as you may suspect there are no people that would rank as very rich.  Do they have less liberty?

I don't have any direct experience with Denmark, but I wouldn't say that they necessarily have less liberty simply due to a high tax rate.  There are many aspects of economic freedom, taxation being only one.  It is possible to have a higher tax burden but still have greater freedom overall (with a less burdensome regulatory state, for example).  Check out this article by Swedish libertarian economist Markus Bergstrom.  He makes a good point about the non-Eurozone countries (which presumably avoid much of the regulatory burden imposed by the EU) relative to the other countries on the continent.  

The core economic truths remain nonetheless - the higher something costs, the less will be demanded.  In the case of labor, as workers become more expensive, fewer of them will be hired, ceteris paribus. To the degree that the Danes are content with their model, may their chains rest lightly upon them.  Living in the glass house that is the modern American economic model, I'm in no position to throw stones.

A quick comparison of Denmark and Sweden from Stefan Karlsson.