Place chicken in a baking dish. Cover and bake for 1 hour in preheated oven. Remove chicken from dish and allow to cool. Remove meat from bone and tear into small pieces.
Meanwhile, mix the cream of mushroom soup, the cream of chicken soup, chili, picante sauce, milk, onion, cumin, and garlic powder in a large bowl.
Spread half the shredded chicken into the bottom of a 9×13 inch baking dish. Cover the chicken with half of the tortilla pieces. Pour half of the sauce on top of the tortillas; sprinkle half the Cheddar cheese and Monterey Jack cheese evenly over the dish. Repeat the layers with the rest of the ingredients.
Bake in preheated oven until all the cheese has melted and sauce mixture is bubbling, 35 to 40 minutes.