The 6mm seating dies come with an alignment sleeve that has a inside diameter of right around 0.28 inches. This is too small for the diameter of the neck on 243 WSSM brass.
To get the 6mm seating dies to work with the 243 WSSM you will need to order alignment sleeve #398559 from Hornady that has a 0.29 inch inside diameter.
Most of my reloading dies are Hornady. I like the seating dies and how they have alignment sleeves to assist in guiding the bullet to align it better... or at least they look like they should be better.
I had a Hornady two die 243 WSSM set, product number 546225. This die set has been great with a resizing die and a seating die. What I have been doing the past couple years is get multiple seating dies per caliber. I do this because when I get a particular load shooting the way I want I don't want to touch the die any more. Because I don't want to mess with the die I get multiple seating dies with one for each load I work up.
So I though I could just by more 6mm seating dies (product #044103). Well that almost worked. What I found was that when I would seat the bullet the neck of the case would get stuck in the bullet alignment sleeve.
The brass is extra thick on the WSSM cases making the outer diameter of the neck too large to fit in the alignment sleeve of the 6mm seating dies.
After a couple calls and emails to Hornady we found the correct alignment sleeve for the 243 WSSM. The alignment sleeve that comes in the 6mm seating dies needs to be replaced with alignment sleeve #398559 for it to work with the 243 WSSM.