In order to compare European and American authors, you need to choose a particular time period or literary movement. For example, we can look at the Romantics. In Europe, the Romantic writers include Percy Bysshe Shelley, Mary Shelley, Lord Byron, Samuel Taylor Coleridge and John Keats, among others. These authors focused on the "emotional" aspects of humans that they believed had been overlooked by the Enlightenment. They were interested in the abstract, the irrational and the magical. They also talked about the beauty of nature and the negative aspects of society.
The Romantics in America shared some of these topics. They were also interested in the value of the superstitious, the abstract and the emotional in life. They highlighted the value of nature as well. However, their views of nature were shaped by the landscapes of America, and the idea of vastness and exploration. The movement, just like the one in Europe, gave precedence to the individual above the social and gave rise to the Transcendentalist movement.