My senior thesis was a comparison between Jane Eyre and the Scarlett Letter. I made the argument that these were the same book -- both had elements of an "excluded woman" and the various social constraints she was forced to overcome. They were reflecting the same idea -- but one did it within a English Gothic environment, the other within the American wilderness. The big clue was that they were published within a year or two of each other on either side of The Pond. Which was better? Neither. They are different flavors of the same essence.
I prefer the rich history that British Literature provides, and I especially appreciate the oldest works in English such as Beowulf or Sir Gawain, but for American students, I think that American Literature and its clear tie-in with our history is more assessable and interesting to them. I also think that the students can more easily see how one literary movement "created" the next: Puritanism to Enlightenment to Transcendentalism to Romanticism to Realism.
As has been said, the answer is going to depend on who you ask. This forum has participants from England and Canada and the US. I hope you will get a response from representatives of each of these places.
Also, if you ask high school teachers versus college instructors versus university professors, you may get three different answers based on what is en vogue at each level and what nation's literature offers the most richly appropriate body of instructional materials.
As an American interested in works from the 20th century, I prefer American literature over English lit and over Spanish language literature as well. However, I do read and intend to continue reading literature from around the world (in translation, I humbly admit).
But, if you'd like a categorical answer, it's my impression that Faulkner is still king of world literature and his second is Hemingway. This is said, of course, in consideration of Shakespeare as the most widely read writer of all time.
The writers of American modernism dealt with themes that still resonate today and, really, still seem like open (cultural) wounds, being taken up again by Coetzee, Morrison, and other contemporary writers around the world.
I would say that it depends upon the reader. There are aspects of both genres which I admire. At other times, I have found myself struggling (given lack of understanding of the setting and ideals depicted). Regardless, each text needs to be judged in its own right.
This is a difficult question, but I guess I would have to say British lit simply because, being much older, it contains more great works, especially those from the middle ages (especially Chaucer) and the Renaissance (Shakespeare, Sidney, Donne, Herbert, Jonson, etc., etc.). Some of the best humorous writing in English comes from those periods, too, and I personally like writing that is simultaneously humorous and morally serious.
Being an American, I prefer reading the literature of my own country. Brit Lit certainly has its advantages, including a much longer history of the written word, as well as the greatest of all writers--William Shakespeare. But I most enjoy reading about the settings and history of the U. S., and our country certainly has a great literary heritage that includes some of the world's greatest writers: Edgar Allan Poe, Mark Twain, William Faulkner, Ernest Hemingway, John Steinbeck, and Carson McCullers, just to name a few.
It really depends on which country you are in which you prefer. Personally, I enjoy British literature because I fell in love with Victorian novels when I was a teenager. I love American literature too, and probably am more widely read in American literature.