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The Lee Pistol factory crimp die has a carbide sizing ring that "post sizes" the loaded round to max allowed size. This will size down any over belling of the case mouth that isn't removed by the seating/crimp die. It also puts a very snug taper crimp on the loaded round. The Lee rifle factory crimp die will apply enough pressure to crimp a non cannelured bullet without deforming the bullet or the case.

edit: The Lee pistol factory crimp die will remove the bulge from brass fired in a unsupported chamber with the "Bulge Buster" attachment a great addition to any pistol reloader's equipment.

I use either Lee or RCBS dies so I can't speak to Dillon/Hornady. I crimp my .223 ammo with a Lee factory crimp die (separate die) all my pistol ammo (.38/357, 9mm, .40 and .45) get run through a Lee carbide factory crimp die. I put a light taper crimp on my semi auto ammo and a medium roll crimp on my .223 ammo and my revolver ammo. Other rifle rounds may or may not get a crimp depending on intended use.