Preheat oven to 350°. Cut out bats from tortillas, using a 4 1/2-in. bat-shaped cookie cutter and pressing a rolling pin over the top to help cut through. Arrange bats on 2 rimmed baking sheets. For sweet bats, brush one panful on both sides with butter but don't season yet. For savory bats, brush second panful on both sides with oil. Combine chile powder and salt; sprinkle over one side of savory bats.
Bake bats until golden, swapping pan positions halfway through, 8 to 9 minutes total. As soon as sweet bats can be handled, combine sugar and cinnamon in a small bag and shake a few warm, butter-coated bats at a time. Serve sweet bats with chocolate sauce and savory bats with salsa if you like.