Since I have never tried a CI dish for pizza I will speak only to the stone type. I have been making Pizza on a WFO for a while. The porous nature of stone tends to wick out the liquids and IMHO will result in a crispier final product. I use a piece of natural granite that was left over from some projects around the house. I use the un-polished side and preheat the stone in my convection oven while I bring my Vision Kamado up to the highest temperature I can muster. 700 degrees +. The key in getting a good spring in the crust, is to get the dome of the cooker equal to the temp of the stone or greater. I make Neapolitan style pizzas. No greater than 10" in circumference, sparse sauce, the best cheese I can find and one or two toppings. Fresh Mozzarella can be a challenge on a thin crust pizza because the cheese will implode it's oil and blow a hole through the crust. Flour on your stone is you enemy as it will burn quickly. Use a peel that is perforated so that the flour can be shaken off prior to loading the pie on the cooker. The true art of pizza is baking and broiling at equal temps. master that my friend and you are a Pizziaola on any type of cooker!
Backyard Disasters are my specialty.
"Tushka" The Black Warrior 24 x 50 offset by TuscaloosaQ, "Libby the Lion" L5000 gasser, and "Vanessa" my Vision Kamado Pro III & "Ruprecht" my Weber Gold OTG
Member KCBS, FBA
Pitmaster at "Sultans of Sting" BBQ Team it's a French thing!