The best bullet puller is a large set of dikes in conjunction with the press. But it does destroy the bullet.
The gripper type, usually with 3 sets of holes work ok if the ammo hasent been loaded very long.
If so use the dikes. The collet type can also deform the bullet if tighten down hard is required.
Years ago when lots of military 06 ammo was available, id use dikes to pull the bullets on the LC match ammo,
then just reseat a hunting bullet.