Another huge difference between the books and movies are in the books, it was a powerful elf called Glorfindel who saved Frodo from the Ringwraiths instead of Arwen in the movie. However the movie screenwriters decided to give Glorfindel's role to Arwen to better introduce and build her character in the movies and especially the relationship between Arwen and Aragorn. And also Glorfindel rarely appears later on in the books so it would be pointless to include him in the movies as an important character just for this scene.