It is very hard to do a comparison when priorities are this different. One of the central questions boils down to: How do you actually measure living standard?
Given that living standard is usually at least partially measured as a function of disposable income it becomes a bit problematic of a measure. The original article notes that there is a bias towards higher earners in the data set:
or one thing, Nordic immigrants to the United States probably came from the better trained, more literate and more ambitious segments of the population
It is perhaps no wonder that the ethnic Danes in the U.S. are relatively high earners, because they are the results of a process of positive selection.
It is thus not very surprising that USA comes ahead as the data is biased. Especially since the median disposable income of after purchasing parity 30,616 in USA versus 27,304 in Denmark according to wikipedia compiled list. While this list is not entirely accurate it is already in favor of USA by about 10 percent. Since we can conclude that the migrants probably are higher earners its more likely that the difference is even bigger than median in a group that is biased to higher pay.
Second point is also noted by the article itself Denmark is a small country which leads to less wealth inequality:
Furthermore, larger countries tend to have higher levels of income inequality than do smaller countries
On top of this Nordic countries rank low in income inequality due to generic policy that actively strives for keeping the disparity low.
So in the end if you have a system that gains certain benefits from equalizing peoples income and somewhat aggressive progressive taxation. Then it is highly likely that the life earnings of your person is lower. On the other hand these priorities give a lot of intangible benefits that are hard to measure and the numbers are hardly fair, a person with lower income may be better of when other factors are considered. But this is hard to prove and in any case easy to hand wave the data as inaccurate in face of hard numeric evidence of simple measurements.
I personally expect USA to beat all Nordic countries with any easily measured index simply because USA is richer. Because I am from Finland I hardly think Nordic countries are a utopia, I can see flaws daily. But the point of the argument is that USA could probably be much better of with a bit softer social policy which the numbers do not measure very well. However this said moving from a low social cohesion to a higher one seems to be challenging, but if any country can reinvent itself in this way USA has the possibility to do so.
PS: I am aware that my citations are weak and i should dig a bit deeper into the subject so take this with a grain of salt if you may.