Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the shredded cooked chicken, whole kernel corn, cream-style corn, sour cream, and mayonnaise. Stir until well mixed.
Add the diced onion, diced green bell pepper, garlic powder, onion powder, black pepper, salt, and smoked paprika to the bowl. Mix thoroughly to evenly distribute the seasonings.
Fold in 3/4 cup of the shredded cheddar cheese and 3/4 cup of the shredded mozzarella cheese into the mixture.
Transfer the mixture into a greased 9×13 inch baking dish and spread it evenly.
In a small bowl, combine the crushed buttery crackers with the melted butter until the crumbs are evenly coated.
Sprinkle the cracker mixture evenly over the top of the casserole.
Top the casserole with the remaining 1/4 cup cheddar cheese and 1/4 cup mozzarella cheese.
Bake uncovered in the preheated oven for 35 to 40 minutes, or until the casserole is bubbly and the topping is golden brown.
Remove from the oven and let it cool for 5 minutes before serving.