Back when I handloaded centerfire rifles I usually went with Winchester or Remington for my brass sources. Used some Federal too, and with my exotic calibers, Norma. I remember the Remington brass being a bit stiff. I felt that the greatest influence on handloading was the choice of bullets and powder amounts, I used different primer brands, more for variety reasons than any assumed accuracy issues.
Got started recently in handloading for .45 long colt. Have been using Starline brass, and experimenting with the 200 and 250 grain bullets, have not used jacket bullets yet. Shot some 200 grainers in Magtech brass that I had, the accuracy was very inconsistant. Often the bullets would go all over the paper, or off of it. Then I would get 3 shots that would be very close. Can different brass be that influencial with accuracy in handloading? I never understood why some shooters said that different primer brands would effect things too?