I read poetry in several languages, and it seems to me that American poetry is different from poetry written in other countries in one particular respect, which is that an American poet is very likely to write a poem about, or in the voice of, a character from a very different walk of life than that of the poet—a truck driver or a politician or a prostitute or a mass murderer. This is almost unknown in the poetry of most cultures, where poetry tends to be about the world the poet lives in. Still, we are not totally different; contemporary American poetry shares with the poetry of all other countries with which I'm familiar a preference for the language of speech over the language of high rhetoric, and—among most of our poets—a preference for clarity of dramatic situation, leaving the mystery of the poem to aspects of motive, meaning, and characterization.
But is American poetry American in some special way? Yes, in the same way that Italian poetry is Italian: it expresses the priorities, prejudices, aspirations, and uncertainties of the culture out of which it comes. If these were not very different from one people to another, we could not use the word culture in this sense. It's for sociologists to tell us, outside the poetry, what these are.
With all the differences, though, a given poem from the hills of West Virginia may have more in common with one from the hills of Scotland than it has with a poem from Minneapolis. The question is a complex and richly textured one, and it would take two or three dissertations to answer it, if it can be answered.