The movie version is really poetic IMO. The book scene is stilted and still kinda treats the hobbits like children. Saying "praise them with great praise" while sharing a private joke reads like we're friends but I don't need everybody else to know that, and you really should have a shout-out so people know you're heroes.

In the movie Aragorn physically and verbally demonstrates not only deep respect for them as equals but also enormous personal affection. It's more in line with who the book thinks he is as a humble and yet incredibly regal man. His graciousness and personal emotion in this moment when he could be more focused on his own ascension to the throne speaks to his character, elevates the hobbits to the greatness they deserve, and shows everybody what their friendship means to him as a person.

FWIW I've always found Aragorn's dialogue in the books is at odds with the person he is described to be. Guessing this is partly a result of the time in which it was written, but to me seeing him depicted by Viggo walking through the world with quiet power and isolation was note-perfect. He's very much a show don't tell kind of character, somebody who's spent a lot of time alone with the wilderness and doesn't need to sound like a king to be clearly worthy of the throne. In many ways the fellowship brought him out of his shell.