Benefits: fast Drawbacks: holding the bird and using an axe or hatchet; making it a clean cut; large volumes of blood spraying out.
For many the historic and only way considered to kill a chook is by chopping its head off. This is a quick method as long as the head is severed completely at the first blow; the bird is immediately unconscious and bodily functions cease.
There are a couple of negatives. One is holding the bird in the right position (you can wrap it tightly in a towel or blanket) and wielding the axe/hatchet with the other. There’s the risk of doing yourself an injury, or injuring someone else if they are holding the bird for you.
Decapitating a bird also releases a large amount of blood very quickly, which tends to go everywhere as the bird will still move due to nerve spasms. Also, if you are killing a bird for meat and need to dunk it straight away into hot water (to loosen feathers to help with plucking), it can get very messy.
Wielding an axe can be difficult and messy