The differences between English Romanticism and American Romanticism are largely due to the national context in which these works were written. England had been a country for over a thousand years by the time its Romantic movement started in the late 18th century. The English people had a long national history and had been a powerful force militarily and culturally for several hundred years. This history, along with the often negative social effects of the scientific and industrial revolutions, sparked a change in their artistic focus. Poets like William Blake, William Wordsworth, and Samuel Coleridge had tired of the rationalistic, scientifically motivated writing of the Enlightenment, and wanted to probe the emotional lives of common people, as well as marvel at the mysteries of nature in terms of its beauty, rather than its physical laws. Poems like Blake's “Chimney Sweeper” and Wordsworth's “She Dwelt Among the Untrodden Ways” looked at how life treated ordinary people, and sometimes it was not a happy thing to see. Shelley's “Ozymandias” questioned England's imperialistic, empire building foreign policy. Coleridge's poetry, particularly Rime of the Ancient Mariner, presented a supernatural vision.
In America, things were different. The country was young, having been colonized and settled less than two centuries before Europe's Romantic Era began. Unlike England, America had no long, well-established cultural history to shape its literature—so America tended to follow what it read from Europe. So why did its Romantic period evolve differently? If America didn't have a lot of history, what did it have a lot of? In 1800 America still had only 16 states and less than six million people (almost a million of which were slaves)--so most of America was undeveloped and unsettled. What America had in abundance was territory, an almost mythological frontier that seemed to stretch out infinitely. America also had more of something than almost any other country in the history of civilization—freedom (although obviously not for those million slaves—theirs would come as the Romantic Era was giving way to the next movement, Realism).
So, as a result of this frontier and freedom, American Romanticism went down a somewhat different literary path. Writers like James Fenimore Cooper wrote about exploration and the beauty of the continent. Ralph Waldo Emerson and Henry David Thoreau helped begin an intellectual movement called Transcendentalism, that espoused the idea that every man was imprinted with the keys to the universe in his own being—you didn't need a scientist to explain life to you, it was there already, provided by your maker, in your own soul. This idea reflected the freedom Americans felt to be their own people.
Of course, Americans also enjoyed the titillating thrill of a good romantic horror story, and Edgar Allan Poe's work echoed Mary Shelley's Frankenstein, but with an important difference. Shelley's Victor Frankenstein had good intentions as he created his disaster—but Poe's characters, perhaps reflecting the darker side of personal freedom, got themselves into trouble in other, less altruistic ways.
That's a lot, isn't it? Break it down to this: Romanticism's development in England was largely influenced by its national history and industrial/cultural/military might. In America, Romanticism was shaped by the frontier and personal freedom.