The effect can vary with the taper of the cartridge design, and how much taper the size die tries to put on the case. For example, my Hornady 308 Win. FL size die squeezes and tapers the brass noticeably more than my RCBS die.
In 308 I have FL dies from Lee(2), Hornady, RCBS, Redding, Forster, and there may be a Lyman buried in my gear stash. They all move the brass differently.
Last edited by mathman; 05/24/16. Reason: added text
