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Point #1: Origin
Neither movie would exist if not for their creator. "Star Wars" was conceptualized by George Lucas; "Lord of the Rings" was written by J.R.R. Tolkien, who created the entire world of Middle Earth. Tolkien's books (starting with "The Hobbit") paved the way for other fantasy worlds to be written. In terms of originality and "who came first," the winner in this category is clear.
Winner: "Lord of the Rings"