Before I pontificate on which cartridge should get a premium seating die, why don't you experiment with your rifles, and see if you can figure out which chamber is more tolerant of runout?
Both are Weatherby Mark Vs, 26" SS barrels and very long throats (as with all Weatherby's, I'm told).
I'm a structural engineer by trade (retired) and I'm trying to view this process from the standpoint of mechanics. To date, I've only used standard 2-die sets (Redding-257Whby; Hornady-300WinM). I've naively assumed these dies, being orders of magnitude stronger than either of the two brass cases, must not have any role in final accuracy. I now question that premise. In fact, it now seems to me the most important thing I could do would be to get bushing-type neck resizers for both. That should provide the best chance for concentric necks and based on what I'm getting from this thread, concentric necks is very important to accuracy.
As said before, the 257 has a very long and slender neck (call it "dainty") and it therefore seems susceptible to non-concentric forming in a standard die. The .300 win mag is a much "stouter" neck but it's also short and so any non-concentricity would have an exaggerated effect when the bullet is seated.
Perhaps cartridges such as the 30-06 with a robust yet more balanced neck might do OK with standard resizing dies...