I have never quite figured out the logic of cutter pans except that they can be substituted for screens (along with disks) and that they have a built-in cutting edge that may eliminate another piece of equipment or be more convenient to use. At the FAQ section of its website, pizzatools.com addresses the perforation issue as follows:
Why are some pans perforated?
Perforated pans are designed to cook pizzas quickly, reducing the amount of time spent in the oven. They offer consistent, uniform heat conduction for a thicker crust with a snap to it. Solid pans are perfect for pan pizza crusts that are thick and perhaps slightly buttery.
Under the perforated cutter pan section, it is stated that the perforated cutter pans are for thick crusts, and under the solid cutter pan section, it is stated that the solid cutter pans are designed for medium to thick crusts. I have a solid cutter pan and have been using it mainly for thin crusts. What is surprising is that when I have done Google and PMQ.com searches on cutter pans there doesn't appear to be a lot on the subject. I have found several perforated pizza pans but, as best I can tell, they don't have the built-in cutting edge.