I've tried different primers over the years. They rarely affect accuracy with a few exceptions.
I've found that the mild primers, like the CCI's, sometimes don't consistantly ignite some ball powders. Federal and Winchesters do well with all types of powder, so I prefer them.
I've found that in some cases, when loading at 70% or less loading density, magnum primers help. My .25-20 is like that, especially with ball powders. Reduced loads in rounds like the .280 and the 30'06 are like that.
Primers are one of the last things I try changing when looking for accurate loads with the above exceptions. First are powder type and powder charges. Second is seating depth. E