It's simple: CoA is what you use to hit Logia's, Defend, and enhance attacks. Like it always has.
CoC: can knock out people with weaker wills, tame animals, split sky (maybe manipulate weather), damage surroundings (uncontrollably it seems).
The only thing I really posit is that when you hit someone with CoC infused attacks (aCoC), they essentially feel exhausted and as if the attack were much stronger than it actually is. But people refuse to believe that the weird as fuck CoC ability list can also include debuffing the target.
People are confused because Kaido remarked at Luffy's usage of CoC, which many baddies have done before. But CoA is the bare minimum requirement for Luffy to hit Kizaru, CoC would be an add-on for extra damage.