Naruto, as the son of Hades, would have some really cool powers. His Rasengan could potentially be infused with the power of the Underworld, making it a much more deadly attack. He could also have the power of persuasion over the dead, which means he could make them tell him secrets or do his bidding. His ability to sense chakra in the Naruto world could be translated into sensing the life force or the 'essence' of beings in the Percy Jackson world. This would give him an edge in detecting enemies, whether they are living or undead.
Since he's the son of Hades, Naruto's powers would be a blend of his ninja abilities and the powers of the Underworld. He might be able to create portals to the Underworld, not just for himself but also for his allies or enemies. His shadow clones could be given special properties, like being able to withstand attacks from magical creatures. He could also have a form of 'death - vision', where he can see how a being will die or has died in the past. This power could be used for both strategic purposes in battle and for solving mysteries. His power over the elements might also change. Instead of the normal five elements in the Naruto world, he could have a connection to the more 'Underworldly' elements like shadow and bone.