I think it would have been cool to see Naruto trained by both of them.
Learn the basics (Genjutsu resistance, chakra control etc.) from Jiraiya. Including stuff like Kenjutsu, and maybe giving him a similar weapon to the Sword of Kusanagi but from the Toads.
Kakashi teaches him how to add variety to his jutsu set, such as innovating with Kage Bunshin, eventually teaching him Rasenshuriken, and mastering his Fuuton in that time.
It would have paralleled better with Sasuke who got all of the above but with his own skill set. They would have been roughly even at that point, and would make more of a balance between them, once they achieved MS and Sennin Modo respectively.