The Naruto story would be very different. For starters, Naruto's character development would be altered. He'd have to come to terms with being the reincarnation of Dante. His goals might shift from becoming Hokage to something more related to Dante's mission in his own world. Also, the power balance in the Naruto universe would be disrupted. Enemies that were once a challenge for Naruto using ninjutsu might be easily defeated with Dante's powers. And the story might involve more exploration of the connection between the two worlds from which Naruto and Dante come.
Well, if Naruto is the reincarnation of Dante in a fanfiction, the story would change in multiple ways. Naruto's appearance might change to incorporate some of Dante's features, like his white hair. His fighting style would be a complete makeover. He'd be using Dante's Rebellion sword and his guns. The story could also introduce new characters from Dante's world, like Lady or Vergil. These new characters would interact with the existing Naruto characters, creating new alliances and rivalries. The overall tone of the story could become darker and more action - oriented, similar to the Devil May Cry series, as Naruto takes on more of Dante's characteristics and the threats from Dante's world start to seep into the Naruto universe.