What I mean is, in the Hierarchy of Sins against Humanity there are entries for "manslaughter", for "murder". However, one might argue that the Kindred are already dead. So, would you argue that causing the Final Death of another Cainite constitute murder? What if the victim is a wight (i.e., a vampire with a Humanity/Path rating of 0, therefore arguably a mindless beast)?
I would say yes, killing another vampire calls for a degeneration roll and may lead to the loss of Humanity.
Vampires (on the path of Humanity, which we're concerned with here) consider themselves, or at least try to consider themselves (at least partially) human - that is what's reflected by their Humanity score. If a vampire strictly and unquestionably believed that vampires are completely dead as humans, said vampire would have to apply the very same thought to herself too, ie. consider herself dead as a human as well. Were she able to do so, it would mean she would have no Humanity left in her either at all (Humanity: 0.) (Once again, we're dealing with vampires on the Path of Humanity only here.)
As for destroying a vampire with a Humanity/Path rating of 0: I think vampire characters have no means of learning the Humanity score noted on the character sheet of a PC or an NPC. They might very well consider said vampire to be a madman, an utter degenerate worse than the worst of humanity... yet they would consider the vampire in question to be a mad, utterly degenerate... human+Beast combination (see the previous paragraph.) And killing a human, even if that human is a walking horror, may lead to the loss of your own Humanity (as you're getting closer to accepting and utilizing the horror's methods... even if to eliminate the horror.)
If the would-be destroyers somehow gained certain, unquestionable, in-game proof of some other vampire's zero Humanity rating and they gained similarly rock solid proof about the impossibility of vampiric redemption (your ST discarded Golconda?), they could probably kill the zero Humanity vampire without risking losing Humanity for the act. But I highly doubt such proof would be available in the stories of most Storytellers.
What would make killing a vampire do to the character mind?
Could the character feel remorse for killing a sentient being with feelings, memories, and its own motivations?
Would an innocent mind be affected after that kill?
If the answer is yes (I think that way), the character must make a degeneration roll to see how much innocent he preserves.
I think the answer is actually a bit more complex than this. Does final deathing a vampire save others? Is the target vampire killing a lot of humans or causing significant human misery? Id adjudge that more as impassioned violation than murder.
Consider the consequences of non-intervention. If the enemy is incredibly powerful, there's little to blame a PC for not acting immediately (survival, risk of breaking the masquarade, etc).