Cat's damage wild life populations?... hmmm as I recall.. a single dog killed 50 something kiwi's in one night.
I also don't remember the last time a pack of "pig hunting cats" chased down a woman and decided she was a chew toy.
What I'm trying to say is everyone is comparing apples and oranges. Dogs and cats are completely different species with different needs and requirements.
Infact, I'd almost go so far to say that individual animals have different needs and requirements.
Anyway, if the cat is on your property and your dog ate it, not your fault. Cat's generally aren't containable.
If a dog came on your property and injured your cat (if that happened to me, that dog would go "missing") that's not your fault and you'd expect the owners to pay for vet bills.
"Expect" though, it's not law to pay... if they were financially unstable for example obviously they probably wouldn't.
Plus I don't think pet insurance covers that sort of stuff.