Peel and devein shrimp; set aside.
Bring broth to a boil in a Dutch oven; add tortilla chips. Remove from heat; let stand 10 minutes. Position knife blade in food processor bowl; add half of broth mixture. Process until smooth, scraping down sides once. Transfer mixture to another container. Repeat procedure with remaining broth mixture. Return blended mixture to Dutch oven; stir in green chiles and diced tomatoes. Set aside.
Melt butter in a large skillet over medium high heat. Add shrimp, onion, and garlic; cook, stirring constantly, 3 to 4 minutes or until shrimp turn pink. Stir into broth mixture; cook until heated, stirring occasionally (do not boil). Stir in sour cream and cilantro. Sprinkle each serving with cheeses. Serve immediately.