There are two main conflicts in "The Legend of Sleepy Hollow." The obvious and external conflict is between Ichabod Crane and Bram Bones, who desire the same girl, Katrina van Tassel. An underlying conflict embedded in the story is the conflict between Enlightenment and Romantic ideals, explains Shmoop.com.
Ichabod is characterized as a weak and greedy man. His most important goal, by all appearances, is to pass through life as comfortably as possible. This goal drives his desire to marry the beautiful Katrina, an heiress. Bram Bones is his opposite in many ways, strong and fun-loving, and he too has decided to marry Katrina. Ichabod, however, refuses to fight Bram for Katrina, so Bram is left frustrated as Ichabod rises in Katrina's esteem.
Bram, however, is not stupid. He uses Ichabod's fear of the supernatural against him by masquerading as the legendary Headless Horseman and frightening Ichabod into fleeing the community. In this section, Washington Irving's intent becomes clear; he is contrasting the rationality in Bram's character with the romantic silliness of Ichabod's belief in ghosts. Irving wrote at a time when the Romantic movement, filled with gothic stories of the supernatural and magic, was overtaking the Enlightenment, a time of scientific thought and rationalism. With this underlying plot conflict, Irving illustrates the power of the Enlightenment over its new rival Romanticism.