13564 is the powder funnel for the lead/plated bullets. It is actually the same one used for the .30 carbine. It bells the case mouth.
13015 is the one for the jacketed bullets. At least the boat tail ones. It fits over the case neck and does NOT flare it. Interestingly, it says on the package it is also the one for the 7.62x39 ("AK") cartridge.

As I am sure you know, there is a dang difference between .308 and .311. Apparently Dillon figures the case neck thickness is sufficient to keep the powder from "missing" the .308 case. Time will tell, for sure.