I have chickens as well and lost birds in past to neighbors dogs, on more than one occasion. Many of my birds are worth a great deal in terms of dollar value and some for personal attachment reasons. When putting value on dog versus chickens lost and potential value of having good relationship with neighbors, you chosen response was not the best long-term option. You just got a little short-term release for exacting some revenge.
I don't think it's a matter of revenge. It's also a matter of public safety. Unknown dogs, in prey drive, can be dangerous. Esp untrained dogs that are roaming loose. Are the dog's possessive? It's pretty easy to get bitten taken something away from your own dog, let alone a strange dog.
Plus, the simple matter is, in most areas it's the law. Dog attacking livestock = dead dog.
It is law here as well. Cool heads should also prevail if long-term relationship with neighbors is to prosper. One of my neighbors is the shooting up sort. He does not generate much sympathy for his losses and he does not have the social stature in public that would promote others to promote protection of his livestock.
If neighbors not known as individuals and no interest in having such a relationship, then continue down this path. Being neighborly was at one time a characteristic attributed to rural populations. What is playing out here is the cold intolerant mess that is a symptom of a society where members react without consideration of consequences. Loss is more than just a few chickens and a dog, it is also social graces.