How would I argue that the Hobbit book is better than the film in a persuasive essay?

This is totally dependent on your own perspective, but there are many avenues that you could pursue in order to illustrate why you think J.R.R. Tolkien's The Hobbit is better than Peter Jackson's film adaptations that have been artificially stretched across three films. For one, you could mention that Jackson takes liberties with the source material, and that the decision to stretch The Hobbit, the shortest of Tolkien's four books of The Lord of the Rings saga, into three movies was purely for financial gain. Or perhaps you could argue that you find Tolkien's prose more immersive than the directorial style of Jackson. Perhaps you enjoy what you imagine when you read the book over what Jackson presents on the screen. However you decide to approach your argument, what's most important is that you make your point clearly and concisely, and convey a sense of authority.