I am using Winchester large pistol primers because they are the cheapest.
Last year I shot about 4000 rounds of Bullseye. I can say for certain that my choice of primer would not have changed any of my misses into hits. I shot an 22 LR indoor Bullseye match this week, and I was using RWS Target Match. If I had been using Red Box Eley, that would not have changed any sixes, sevens, or eights, into tens.
I do believe that if you have a marginal ignition system then the best choice is Federal primers. Federal is proud of having the most sensitive primers on the market, I used to use them, but they got expensive.