I'm American and Italian and have lived in Europe and the U.S. I've found that your question applies to both Europeans and Americans. The biggest enemy to cross-cultural understanding is provincialism. Every country has contadini/country folk and self-aggrandizing elitists.

One thing that bothers many Old Worlders is when Americans say, "I'm Swedish, I'm Italian" or "I'm German". This is especially true when the ancestor in question is several generations removed. I'd recommend just skipping that whole conversation because Americans are generally scoffed at. I don't approve of the attitude because I find it unnecessarily condescending. This shows a lack of understanding of American culture: a culture where many of its citizens have conflicting or amalgamated senses of identity. It seems that it is easy to take for granted the notion of one's ethnicity and nationality being the same.