One interesting crossover could be a battle between Naruto's ninjutsu and the Turtles' martial arts skills. For example, Naruto could use his Rasengan while the Turtles use their signature weapons and combat moves. Another aspect could be the sharing of knowledge. The Turtles might learn about chakra from Naruto, and Naruto could gain some insights into their street - smart survival tactics in the sewers of New York.
Well, in some fanfictions, the characters might team up to fight a common enemy. Maybe Orochimaru from Naruto decides to invade New York and the Turtles and Naruto have to join forces. The Turtles' sense of humor and their brotherly bond could contrast with Naruto's determination and his own complex relationships within his ninja team. They could also exchange their cultures. The Turtles could introduce Naruto to pizza, and Naruto could show them some cool ninja gadgets from his world.