Pets aside, as a few states are starting to adopt differing standards for pets, fair market value (FMV) of property is always a consideration when suing for damage to property. The basic rule is that you are entitled to the lesser of the FMV of the item just before it was damaged or the cost to repair it back to the condition it was right before it was damaged. Whether the item was completely destroyed or not doesn't change that. For example, suppose I have a chair that my neighbor breaks through negligence. The chair is not completely destroyed, it merely needs repair that will cost $50. Unfortuantely for me, that chair only has a thrift store (fair market) value of $25. Because my chair is only worth $25 — and thus I could go out and get a replacement for $25 — my maximum recovery from my negligent neighbor is $25. That's true even though I elect to pay $50 to have it repaired because I really liked that old chair. The fact that I had an attachment to that old chair is a noneconomic factor that does not get compensated for in my claim against the neighbor.
The classic common law rule is that animals (including pets) were treated as mere property and that same rule would apply. In the majority of states that still retain that rule, that means that there is little to gain from suing for death or injury to a pet since pets often have no market value — it is tough to even give away many pets particularly since one can get a pet at many shelters basically for free. Some states have started to change their rules for pets to recognize that they have value beyond being mere property, and in those states it may indeed be possible to sue for for more than just the FMV of pet; that is, it may be possible to get noneconomic damages for the loss or injury to a pet.
But it appears that Texas is not one of those states. In 2013 the Texas Supreme Court considered that very issue and elected to adhere to the long standing rule in the state — dating back to 1891 — that animals, including pets, are property and that the rule applied is that recovery is limited to FMV of the animal (if there was any value) or to any special economic value/benefit that the animal provided. Under that rule, the limit on recovery for most pets will be nominal; they have little market value and provide no particular economic benefit to their owners. But some pets, like some service animals, will allow for greater recovery because they do provide an economic benefit like allowing their owners to work, etc. Specifically the court said:
The “true rule” in Texas remains this: Where a dog's market value is unascertainable, the correct damages measure is the dog's “special or pecuniary value” (that is, its actual value)—the economic value derived from its “usefulness and services,” not value drawn from companionship or other non-commercial considerations.
We recognize that the benefit of most family dogs like Avery is not financial but relational, and springs entirely from the pet's closeness with its human companions. Measuring the worth of a beloved pet is unquestionably an emotional determination—what the animal means to you and your family—but measuring a pet's value is a legal determination. We are focused on the latter, and as a matter of law an owner's affection for a dog (or ferret, or parakeet, or tarantula) is not compensable.
Strickland v. Medlen, 397 S.W.3d 184, 192–93 (Tex. 2013). The Court stated that it was for the state Legislature to broaden this rule to allow for noneconomic damages for injury or loss of a pet. So far as I can tell from my search, the legislature has not yet done so.
So indeed, the FMV of the pet, and any economic value of the pet, are still important as that determines the maximum that can be recovered for injury to or death of a pet in Texas, as stated by the Texas Supreme Court above.