The heavier the wire the more predators it will stop. The smaller the holes, the more predators it will stop. And you are right. How it is attached and what it is attached to makes a big difference too.
Most of the stuff that we call chicken wire is pretty thin gauge wire, maybe 19 to 22 gauge. A medium to large dog, coyote, raccoon, or maybe a determined fox can just rip it apart. It may stop a skunk or possum but it really doesn’t offer that much protection against a larger stronger predator. There is some stuff out there that is made like chicken wire but is made from heavier wire. It will stop more predators so it offers more protection. But there is no way to really answer your question. The heavier the wire, the smaller the holes, and the better it is attached the more protection it will offer.
The same is true for hardware cloth or other welded wire, not just chicken wire. There are things out there that can rip thin gauge hardware cloth apart too.