I don't really have a baseline in Europe to fully answer your question, but there are a lot of common misconceptions in the states perception of Native North America that I can address.

First of all, there is a very common idea that everyone living north of Mexico were nomadic hunter-gatherers. In fact, large portions North America were inhabited by sedentary agriculturalists. This includes much of the US Southwest/Mexican Northwest (Sonora/Chihuahua/New Mexico/Arizona and parts of Utah and Colorado) as well as most of the Mississippi, Ohio, and Missouri rivers (and tributaries) along with much of the Southeast and other parts of the East Coast. You also have sedentary foraging societies in large parts of the Pacific Northwest. These agricultural societies faced many of the same hardships that farmers everywhere would face.

Secondly, the idea of native people in North America living in an ideal state of balance with nature is very much the product of European thought from the 16th century onward rather than a true reflection of life in North America. Jean Jacques Rousseau is perhaps to most famous of these thinkers, credited with the invention of the "noble savage" mythology that posits that Native Americans were mobile, hunter-gatherers who lived without property and so had the best of lives: a life without property and consequently a life of plenty and without strife.

In reality, this perception (while totally ignoring a lot of the societies I already mentioned that don't fit this ideal) tells us more about the desires and compunctions of Europeans, especially in the 18th and 19th century than it does about the actual lives of Native North Americans. In other words, this idea of the "noble savage" is very much a critique of hierarchical European societies more than it is a true reflection of Native American life. It is a romantic notion of what life could be rather than an anthropological description of actual lifestyles.

This perception was so widespread that it entered popular imagination and is still very much alive in the present. Rousseau's "noble savage" is echoed every time you hear someone talk about Native Americans being "one with nature" or otherwise living lightly on the land, or whenever you hear anyone touting the egalitarian lifestyle of Native Americans as an ideal to aspire to. Again, this is more a reaction to modern capitalist society with a desire to return to a "simple" life, rather than appreciating the actual complexity of Native American life.

Edit: All that said, we can't really talk about Native American "commoners" north of Mexico because, with the possible exception of Cahokia, there were no full state societies in North America. That means no kings or nobility, though that certainly doesn't preclude there being people in positions of power with differential access to wealth and resources. If you think of living in a state society as inherently odious (as some of these European philosophers did when romanticizing Native American lifestyles) then certainly it seems that Native North Americans had it better, but the types of society really aren't totally comparable.