In a large bowl, combine the shredded chicken, cheddar cheese, Monterey Jack cheese, bell peppers, red onion, garlic powder, cumin, chili powder, salt, and black pepper. Mix until well combined.
Heat a large skillet over medium heat and lightly coat with cooking spray or olive oil.
Place one tortilla in the skillet and spoon about 1/4 cup of the chicken mixture onto one half of the tortilla. Fold the other half over to create a half-moon shape.
Cook for 2-3 minutes on one side until golden brown, then carefully flip and cook for an additional 2-3 minutes on the other side.
Remove from the skillet and repeat with the remaining tortillas and filling.
Cut each quesadilla into wedges and serve warm with sour cream and salsa on the side.