To the question as to why you might feel more moved by a pet's death ... I have given considerable thought ... and might add my (only my) personal perspective.
Pets, whose eyes worship you every minute of every day, make you laugh, worry you ... and call upon you for all aspects of life ... can have importance in your daily life ... more present than any person of much less interaction. I don't believe you are making an evaluation as to the worth of human versus animal here. I think you are asking why am 'I so moved by this creature's death'.
I've got some years. I've lost my people. I've lost my pets.
With people, somehow you are not alone. They may know they are going, the medical team knows ... and only rarely are you the one to say "Do it."
With a pet, they do not know. They trust you. You are making the decision, driving them to their kind end or inviting the vet in. It may be a sense of betrayal for you ... towards the unsuspecting, trusting ... the big brown eyes of trust.
Well, I think the biggest expense I have gone to was a $45 worth of McDonalds on the way to the vet's. Alternatively it has been pizza ... or buttered toast. My mum always, most lovingly, said that dogs are guts. In my long life, I have had only two dogs who would pass on a milkbone to be with me. I am OK with that. You can see that I have been lucky enough to see my loved dogs to their end of old age while they still had appetites, but failing bodily in every other way. I like that they had health enough for hunger when they slept finally.
I never make the decision on the night before. I sleep. The vet is aware that it will be coming shortly, and I wake up in the morning and call in, hit the treats big time ... and then ... well, that's it.
My hope is that every dog hears from his person "Good Dog, you are a good dog" as that kind last sleep falls.
I know I am a sap.
Susan