I was a pizza nut for a few years. I went overboard for a while. I started with the kitchen oven with a stone, then a steel plate, and then to a komado and eventually, I bought a used propane fired, rotary table, kiln-like, oven called a 2Stone which could reach well above the ~850F needed for old world Neapolitan style. There's a lot of tricks you can do with these bbq attachments, but the challenges of controlling temperature with a charcoal fire are a bit much for the occasional pizza enthusiast. Today, there are so many better choices in personal outdoor ovens, even indoor countertop ovens, that a bbq oven is not the best choice for consistency. Some of the latest 120v countertop ovens can even do the Neapolitan temperatures.
If I were to give generalizations, I'd say higher temperatures with shorter cooks, makes for more tender crust. So, if you said you like NY style pizza, you want to cook around 500-550F. Neapolitan style with cook temps around 800-850F and 60-90 second cook times, makes for a much more tender crust than even NY style. Just keep in mind that Neapolitan doughs usually don't have added sugar, which will burn more easily at those temperatures. If you're using ready made dough from a store, you might not be able to cook above certain temps due to the sugar added. Longer cook times equal drier and crunchier crust.
For someone looking to go all-in on pizza, pizzamaking.com is a great place to learn.
