In a small bowl, combine cream cheese and powdered sugar; stir with a whisk.
With clean hands, break up the angel food cake into large pieces (about 6 cups total). Place in the bowl of a food processor and pulse until fine crumbs form; transfer crumbs to a large bowl.
Add the cream cheese mixture and blend until a dough forms. Shape into 1-inch balls and insert lollipop sticks. Transfer to a large plate and refrigerate for 20 minutes.
Place the dark chocolate and white chocolate chips into separate microwave-safe bowls. Heat one bowl at a time for 30 seconds. Remove and stir until chips are melted and smooth (you may need to microwave for another 20 seconds). Immediately remove pops from the refrigerator and dip into either chocolate bowl; sprinkle with desired toppings. Serve immediately.