This discussion is so heartbreaking. Not only do you have to try to be accurate with decapitation or neck breaking, you have to live with the image and experience.
It is heartbreaking and also necessary. If people are going to own livestock (or "petstock" as some of us say), people need to be able to plan for humane culling (as much as I love my hens, I'm not taking them to the vet.)
The killing cone/tree lopper method that
@coach723 linked to earlier in the thread is what I have used and will continue to use. It is fast, hands-off, and there's no "accuracy" needed (as long as the loppers are positioned around the chicken's neck). It is pretty fail-proof. Is the image painful? Yes. Is it more painful than the image of a sick animal suffering needlessly? No.
I take solace in knowing that I gave the hen the best life possible and did what I needed to do when she had an incurable illness/injury. I believe it is irresponsible to raise chickens if you aren't also mentally prepared to end it's life (or have a plan for someone else to do it) quickly and humanely when necessary.
There really should be more advocacy for humane, affordable, at home euthanasia.
I think almost every experienced chicken-keeper in this forum advocates for humane, affordable, euthanasia at home. Cervical dislocation or decapitation are the most humane, affordable methods available in the at-home setting.
I think I gave her 3 hydrocodones left over from a dental thing. I can't say whether she suffered or not, but she was definitely dead in the morning.
I would argue that this method is riskier (in that it may or may not work), longer (who knows how long it took for the bird to die or if it was painful?), and far less "accurate", than decapitation. Did you spare yourself from the disturbing "image"? Yes, but as others have said, humane culling is not about making the human feel better, it's about what's best/most humane for the animal.