When a cop kills a dog, while perhaps regrettable, the dog is just “property”, so it’s not a big deal. Pedigree, training, cost to replace, and value to the owner are irrelevant – even when quantifiable.
But if one kills a police dog, they won’t be charged with destroying police property. No way. In most jurisdictions, the dog is considered nearly equal to a human officer, and felony charges will follow.
Just one more example of how some of us are more equal than others.