I find this a very interesting sequence, not just because it's a bit different in the films to the books, but because it changed dramatically between Tolkien's first draft of the story, and the published version. In published book, this section isn't told in the third person. Instead, it's recounted by Legolas and Gimli, to Merry and Pippin, on the morning after the battle. The Bakshi film didn't cover that part of the book. In the Jackson film, we see the whole action.