Crevecoeur's letters and the Declaration are both statements of the positive themes Americans believe in and, either through direct statements or by implication, the negative aspects of what would soon become the United States.
Crevecoeur is correct in his analysis of the manner in which the differences among Europeans underwent a kind of leveling process in the New World. The European nations had generally been at each others' throats since time immemorial. There had been endless hatreds and divisions resulting in the institutionalized mass violence of war, exacerbated by religious differences both before and after the Protestant Reformation. In Crevecoeur's view, both national and religious diversity has become insignificant in the New World. It no longer matters which nationality or religious sect one belongs to.
Crevecoeur does not seem to recognize that this amicable feeling among the European immigrants was achieved partly (some would say mostly) at the expense of non-white peoples. The differences among the whites didn't matter because both Native Americans and African Americans forcibly brought to the New World were more different to the Europeans than the Europeans were to each other. Crevecoeur, however, does note the degree to which the Native peoples were undergoing a gradual obliteration, due as much to their lack of resistance to the diseases the whites were carriers of as to the deliberate efforts of the Europeans to exterminate them.
The Declaration of Independence expresses ideas that correspond to Crevecoeur's themes. Unfortunately, the most famous clause in the document, the principle that "all men are created equal," was put into practice at that time only with regard to those of European descent. In the lead-up to the Civil War, Southerners claimed that this was the real meaning of the statement: that all white men are created equal. Yet if this had been the intended meaning by Jefferson, Adams, Franklin, and the Congress as a whole, why didn't they write it that way? Even if this was the subtext or the implicit meaning, the fact that it was not stated as such shows that Jefferson and the others knew it was wrong to exclude non-whites from the concept of equality. Jefferson had, as we know, wished to include a passage against the slave trade, but Congress removed it. Though his having written it was an indication of the hypocrisy that dogged Jefferson his entire adult life, just the fact he would write this to begin with proves he knew slavery was wrong.
Still, the absence of any attempt to deal with the slavery issue, the oblique mention of it in terms of "domestic insurrections," and the explicit condemnation of the American Indian are unfortunate and tragic factors that compromised the Declaration. They were a mirror of the flaws in American society. In the same way, Crevecoeur's understanding but lack of empathy for the indigenous peoples also reveals the schizoid character of America.