Unfortunately there does not seem to be very good industry standards on either the caps or the nipples. A Remington #11 is clearly not the same size as a CCI #11.
Also the nipples themselves can vary from gun to gun, even within the same manufacturer and model. I recently bought a brand-new Pietta 1860 Army, and this revolver would only function with Remington #11 caps. Unfortunately the only caps I had in quantity were CCI #10's. However I had a spare set of Pietta nipples from another older Pietta 1860, and when I test-fitted a CCI #10 on them it was perfect!
The cap needs to fit tightly on the nipple - if you have to pinch or squeeze the nipple it's not fitting right - and it needs to fit far enough on so that the priming compound inside the cap is against the top of the nipple so that the hammer strike can set it off.
Just my opinion, but I kind of like the CCI caps because they have a longer skirt, which seems to help keep them in place and provides a better gas seal against the nipple. Some nipples, however, have a more pronounced "cone" shape, and the long skirt on the CCI cap may bottom out against the taper of the nipple before the cap is fully seated. If that's the case, one technique is to chuck the threaded end of the nipple in a drill or drill press (don't chuck it on the threads, however), and hold a fine file against the shaft of the nipple. Remove just enough metal until the caps can be slid on and friction holds them. If I were going to do that, though, I'd buy a spare set of nipples and modify them. Heck, you may find that the replacement set works fine with the caps you have.
Keep in mind that my comments are written from the point of view of a revolver shooter. But also understand that having the caps fit correctly on the nipples is very important with a revolver. One thing that can happen with a revolver is a chain-fire, wherein when you fire the revolver several chambers may go off at once (which is why revolving-cylinder cap-and-ball carbines never became popular). It was always thought that this was due to the flash from the gap between the barrel and cylinder going down through the mouth of the cylinder past the ball and setting off the adjacent powder charge. A very good argument has emerged, however, that it may be more likely to occur from the nipple end, due to unfired caps either falling off under recoil or by the flash getting under the unfired cap and setting it off.