(random image found online) this versus both being double wall any reason to go for one instead the other? is the airflow side help doing something or it's doesn't do anything?
The bottom picture will give you higher flue temps, which will help keep creosote accumulation down and give you a better draft than the other stuff. I've not seen the stuff in the top picture before.
I also assume having airflow / slot could reduce the benefice of double wall clearance reduction with combustible?
one would tend to think so. but then again heat shields on the stove are open so??? or the suggested practice of a wall heat shield that is spaced away from wall by an inch or better open top and bottom.