Like IgneusJotunn, I have played oWoD extensively but have never played any of the nWoD.
But this seems almost system agnostic. They are running into moral ambiguities and then balking. That may not be a bad thing. There are several approaches I think would be good, and I would recommend possibly using all of them on different missions.
Let the soft solutions work at least some of the time.
It sounds like if they see even a hint of good in the monster, they want to save them instead of killing them. Perhaps at least some of the time that is possible. Perhaps the target can be cured if a vampire (if you allow that as storyteller), or taught to live peacefully (with monitoring) in human society. Perhaps they can even be turned to a force for good and become an ally for the players.
This gives them what they seem to really want and lets them occasionally have a true, clean, and absolute victory. Not something that should happen often in WoD, but occasionally it can be very good.
Give them enemies that are pitch black.
Sometimes the enemy could truly be pitch black with no redeeming or sympathetic characteristics at all. Of course narratively this risks creating more of a stereotypical villain who is flat and two dimensional. But every so often that isn't a bad thing. In real life, there are some truly awful people out there, and in fiction you can take that to an extreme and strip off every sympathetic quality from them.
You may have a vampire that sees humans as cattle to be eaten, used, and nothing more and has no redeeming characteristics in dealing with them at all. This one actually does want to hurt them and may even torture his victims before eating them because he thinks it improves the taste.
In short, occasionally give them one they can feel absolutely good about killing.
Give them moral dilemmas and let them face it head on.
Sometimes, you need to choose the lesser of two evils. Imagine a recently turned vampire is still protecting and even caring for their own child. But in their desperation and driven by their urges, they have taken to killing victims for both their blood and their money. In life, the vampire was a single mother working a low paid job trying to make ends meet, but now she has taken the power she received and is getting vengeance on everything that she thinks wronged her before while leaving a trail of corpses, mangled and disfigured partially to hide the fact she devoured their blood.
This character is in many ways sympathetic, and has redeeming qualities. Killing her means turning the child into an orphan and the vampire probably feels fully justified in her heinous actions in a sympathetic way. But perhaps this one can't be redeemed. She enjoys being a vampire. She doesn't want to turn back even if it's possible, and she doesn't want to change her ways.
Killing her harms the child and she is sympathetic rather than having a truly black heart, but she can't be saved. Killing her is the lesser of two evils. The PC's must face that dilemma and make a decision, knowing that they are causing harm no matter what.
It's not hard to take it even further. Perhaps a child is being used as a puppet, but capture would be nearly impossible and it will fight to the death to continue on its mission. They must either kill the child, who is truly innocent, or allow the child to do the bidding of its evil master, at least until they can track down the evil master itself. Do they prevent the great evil but get their hands dirty killing a child, or spare the child but passively allow an evil action? Either way, they go can go after the puppet master later, but only after they fact that choice which will help define their characters...