rfwobbly +1 with a priviso:
With the Federal 'family' of cases (FC, Speer, *-*, CCI) you will get a different crimp than you will with Winchester thickness cases (Win, WC, PPU, R&P). The difference is small, but noticeable on a single stage or turret press when pulling the handle. I measured .001 or slightly more difference at the case mouth, but I know that a dig caliper has up to +/- .001 error.
With my turret press , without changing the sizing or taper crimp die, an FC case will seat a bullet .002-.003 deeper than a Win case will seat it. I have checked this many different times and it is 'consistent'.
In reality, it will make no significant difference for the crimp; but for me it's worth knowing there is a difference in the cases..