I shoot 7TCU out of an XP-100 in IHMSA and NRA Silhouette. After I dialed in my brass, bullet, and powder, I tried 4 different primers at 100 yards and at 200 yards. Some primers doubled my group size. One cut it in half. I didn't shoot just one group of each either.
My buddy and I have DW Revolvers that are consecutive serial numbers. Made on same machinery and completed on same day mid week. (Custom order). Shooting same bullet, brass, and powder, my load is 1.5 grains lighter with a Remington 7 1/2 primer vs his use of the WSR primer. This is to get same velocity and accuracy.
Yes, primers make a difference....a lot of the time. They can take a mild load and make it a WILD load. Do your homework.
Steve