I remember watching animal injury cases on "The Peoples Court". If the animal died, Judge Wapner would give the owner the cost of the animal. If the animal lived, the owner would get the cost of vet bills. What I learned was, if my dog attacked the neighbors mixed breed cat, make sure the cat is dead.
The vet bill part probably varies by state. After all, there is a principle of “mitigation of damages”, so that, theoretically, spending $5000 on a $10 cat is unreasonable as a legal matter, and not compensable.