Anyways, lets not hyper analyze the manga and come up with bullshit.
There are 3 main techniques regarding CoA:
- hardening
- barrier
- internal destruction
There are 3 main techniques regarding CoC:
- knocking out fodder
- coating
- barrier
There is evidently a distinction between a CoC barrier and a CoA barrier, that being that a CoC barrier is much stronger. However you don't need to use barrier to use ACoC, as we saw with G5, where Luffy just used CoC coating without the barrier(until bajrang gun).
This is basically what the manga tells us. In general, barrier is portrayed to be stronger than hardening/coating, and internal destruction is portrayed to be stronger than barrier. But this might not necessarily be an absolute rule. Mihawk's hardening is probably stronger than Luffy's CoA barrier.
I think trying to derive any more from this just leads you into developing headcanon, like Root's shit about the black rings.