Compare the comments Emerson makes about “Self-Reliance” with the comments Crevecoeur made in “What is an American?” How do these views of...

Emerson's "Self-Reliance" celebrates originality and nonconformity. He was opposed to people imitating others and famously wrote:

There is a time in every man's education when he arrives at the conviction that envy is ignorance; that imitation is suicide; that he must take himself for better, for worse, as his portion.

Emerson believed that true genius lay in following one's unique instincts and proclivities and not in copying others. 

Emerson also believed that Americans should not emulate Europeans but should instead cultivate what made them special. He wrote,

It is for want of self-culture that the superstition of Travelling, whose idols are Italy, England, Egypt, retains its fascination for all educated Americans. They who made England, Italy, or Greece venerable in the imagination did so by sticking fast where they were, like an axis of the earth.

In other words, Emerson believed Americans should not try to imitate Europeans, as Europeans became great by fostering what was special within their own cultures. If Americans wanted to become great, Emerson thought, they should stay on their own land and cultivate what was uniquely American.

Similarly, Crevecoeur, a Frenchman, was in awe of the unique spirit that he felt animated America. He wrote of the visitor to American shores: "He is arrived on a new continent; a modern society offers itself to his contemptation, different from what he had hitherto seen." Crevecoeur noted the distinctiveness of American culture from European culture and celebrated this distinctiveness.

Crevecoeur, unlike Emerson, believed Americans had surpassed Europeans' greatness. He said of Americans:

Everything has tended to regenerate them; new laws, a new mode of living, a new social system; here they are become men: in Europe they were as so many useless plants, wanting vegitative mould, and refreshing showers; they withered, and were mowed down by want, hunger, and war.

While Emerson believed each person should cultivate greatness where he or she lived and that Americans and Europeans were each great in their own way, Crevecoeur believed Americans enjoyed a unique sense of freedom and liberty that was far superior to what Europeans had. 

Americans today do not tend to want to emulate Europeans and generally believe in what is called "American exceptionalism"--the idea that Americans have a unique sense of freedom and a particular destiny that is special in the world. Therefore, modern Americans' self-conceptions could be generalized as  similar to those of Emerson and Crevecoeur.