Without a doubt, CLR and other synthetics are much better for modern firearms. The need for solvents has pretty much gone to the wayside. Even though some powders burn "dirty", they are still much better than ever before.Old school practices in cleaning had you "Oiling the bore". Having oil in the barrel when you shoot leaves carbon deposits as the oil burns. All my barrels are swabbed with windex window cleaner so that I have no oil in the barrel.
I shoot 338L and 270wsm for 1200meter and under. With the hundreds of rounds I send a month, I still do not use any solvent based cleaners. A light coat of synthetic Breakthrough, and I have flawless results. I'm getting 9,000 to 12,000 rounds per barrel so I don't argue with the results.
I do use all copper bullets (Barnes) in my hunting rifles. After anywhere from 250 to 400 rounds, I will begin to see a very slight drift in my groups at 300 to 400 meters. That is when I do a copper solvent KG-12.