It is always a good idea to step your charge down a hair (5% is probably good) and work up the load again with any change of components.
Having said that, there is little difference between the performance of most primers on the market today. So, yes, a CCI large pistol primer is going to work just like a Winchester large pistol primer, just like a Federal large pistol primer, etc.
Aside from fairly minute differences in "hotness" between brands (which some folks do notice in comparing HIGH precision loads) the only other difference is that some primers are known to have a harder metal cup than others. A lot of military semi-autos and automatics (like SKSs, AKs, etc) that use a floating firing pin might call for a hard primer to prevent slam fires. Some revolver shooters looking for better reliability with lightened mainsprings in their guns may want a "softer" primer (Federals) so that they don't get misfires.
If those conditions don't apply to you, don't stress too much about the brand of primer.
HOWEVER: Don't screw up and try to exchange pistol and rifle primers (the dimensions are different) or use a Magnum primer when a standard one is called for (until and unless you know EXACTLY what you're doing).
Good luck!
-Sam