I don't think, with todays quality control standards, that any brand is more accurate than another in a given rifle. Some will shoot more accurate with a given load though. I've done some small scale tests with different primers (manufacturers and standard vs. mag), using the same loads, and I've seen groups open and close with the different primers. Their was a difference in the velocity in both extreme spread and standard deviation as well.
If you have an acceptably accurate load worked up for your rifle with the CCI's I'd keep using them. If you want to tinker with changing primers I'd recommend switching between standard and magnums first.