A blockbuster about Elvis Presley should be the be-all, end-all of rock biopics. And considering all the gaudy kitsch associated with the King of Rock and Roll – Graceland! the pink Cadillac! those jumpsuits! – Baz Luhrmann, with his flair for the over-the-top, seems the perfect choice to take the Elvis story to the big screen. So does it pay off? Yes it does, although Elvis the movie is more subtle and sad than you'd expect. Luhrmann still adds loads of visual whimsy, but it's nowhere near the sensory overload that Moulin Rogue! was.

Most biographical dramas opt for either the cradle-to-grave approach or the "key moment in the subject's life" approach. Elvis sort of splits the difference: after some fleeting scenes of Presley's childhood and early exposure to hip-shaking music by way of black bluesmen and Pentecostal revival meetings, the film mostly centers on three key chapters in the singer's life: his overnight stardom in 1955-1956, his "comeback" TV special in 1968, and his Vegas years. The rest of it – the movies, the Army, even his relationship with his wife Priscilla – is handled sparingly. And through it all is his relationship with his manager Andreas van Kuijk, the Dutchman who posed as a Southerner and dubbed himself "Colonel Tom Parker".

Much of Elvis does indeed center on the Presley/Parker relationship, and it will either make or break the movie for you. Casting Tom Hanks as the crooked "colonel" was a risk – it's an unusually villainous role for the actor, who dons a Dutch-ish dialect and wears so much fat and bald makeup that he resembles LBJ more than Parker. Some audience members simply won't buy him in the role. As for me, I thought he was all right. Not great, not terrible. And in a sense, a film this big requires a big star, and since the little-known Austin Butler plays the title role, Hanks's celebrity is needed to justify Luhrmann's grand ambitions. In other words, if you put an unknown Dutch actor in the role, no matter how authentic his performance was, Elvis would seem a less necessary movie.

As for Butler, he's a revelation. He's so good that at times you forget that he doesn't really look much like Presley. It might be a star-making turn or it might be a one-hit-wonder, but his work is energetic and real. Even someone who won't like this film would have a hard time knocking Butler's performance. And the casting of smaller roles is spot-on: Helen Thompson is a dead ringer for Presley's beloved mother Gladys, and Alton Mason and Yola are jaw-droppingly great as Little Richard and Sister Rosetta Tharpe, respectively. One plus about Elvis is that Luhrmann makes a strong case for Presley's appreciation for black music, and the fondness his black contemporaries had for him. Over the past couple of decades, many younger people have reframed Presley's legacy as that of a racist culture thief. Elvis reminds us that he was effectively the Eminem of the 1950s: liked and respected by most black musicians even as they knew – as this film acknowledges – that he owed his superstardom to his whiteness.

All in all, I enjoyed Elvis very much. Perhaps surprisingly, what I liked most about it was its focus on the business end of show business. Usually in a music biopic, the bulk of the story is about the singer's struggles with drugs and/or romance; the money men only pop up in a couple of scenes, greedily rubbing their hands and taking advantage of our fragile hero. But because Tom Parker was so central to Elvis Presley's professional life, this film reminds us that Presley was no dewy-eyed innocent when it came to his career. Parker stuck him in a gilded cage, but Presley was definitely ambitious and enjoyed all the money that he made. It was a toxic relationship, to be sure, but more symbiotic than parasitic.