Dave, in looking at Accurates loading data, I see that they list Win/Rem/Ched primers. I know that Winchester and Cheddite are interchangeable. I don't know about Remington. I do know that the CCI 209 primers are milder and for some low-pressure loads I use they are recommended. I use information from the 16 ga Reloaders Group, and all of those loads are pressure tested and velocity tested. For 12 ga and 20 ga I use the new Lyman's Reloaders Handbook, and like I stated earliler, using the same componants and just changing the primer could result in a lot higher pressure.
Also in regard to what Mike said, I have new primed Cheddite 16 ga hulls with Cheddite 209 primers. I have de-primed some so that I could use CCI 209 in them, and have had no problem with them "falling out", or being loose. Like I stated before the Cheddites and Winchester primers are "stepped" in size whereas the CCI 209 and Remintons are straight.
Fiocchi primers are bigger in diameter, never used them so don't know their size. So I can see a Winchester primer being loose or falling out. They sell a tool to ream out your shell to use them, also have a tool to re-condition your primer hole so the primer is tight.
