I think the CCI Reenactor musket caps have a weaker charge. Some of the other fellows may know the rest of the story, but as I heard it, somebody got a cap fragment in his eye shooting his gun at a reenactment and sued CCI. They came up with these weaker caps that would be less likely to fragment. That's the way I understood it. Anyway, a lot of people find ignition with these is less reliable, and the really skilled shooters evidently find the cap does make a difference in downrange performance.
I bought a new Armisport M1842 musket some years ago. The seller was working with a gunsmith who specialized in defarbing, so I paid extra for the "defarb package." The gunsmith did a great job. I did a routine, preliminary cleaning of the gun and took the it to the range and loaded 'er up. When I went to cap the nipple, powder grains were visible in it. I thought that was odd, but shot the gun with moderate loads and had no issues. I was using CCI Reenactor caps. However, when I got home and cleaned the gun, I found the gunsmith had bored out the flash hole in the nipple. Evidently this is standard procedure for guns for reenactors, who were that gunsmith's primary customer base. I replaced the nipple with one that had a normal sized flash hole.
I think the CCI Reenactor caps really are intended for reenactors. With the bored out nipples that they use, powder can get a lot closer to the cap flash, so detonation of the main charge is no problem. However, if you shoot bullets or balls, the backpressure resulting from the powder charge overcoming the inertia of the projectile can blow back through the bored-out nipple and kick your hammer back to half-cock. I've heard sometimes worse things can happen.
Anyway, if the CCI caps work in your gun firing live rounds with a standard nipple, there is no reason not to use them. If it were me, I would not bore out the flash hole to make the caps work better... I would get hotter caps. Safety issues aside, you can lose velocity due to the gas leak through an oversized flash hole. If you get a chance to pick up some RWS or Scheutzen caps, you may want to try some of them and compare results, anyway. See if accuracy and performance improve.
Best regards,
Notchy Bob