I would think that a bird that is caught and killed immediately or stunned immediately would have about the same amount of "stress". Think about it. If I grab my chicken and it's head is lopped off right away, it experiences stress for what - 30 seconds or less? However long it takes to get her to the stump and her neck between the nails and then it's over. If I grab my chicken and get her positioned to "stun" her, she's being held for roughly that same amount of time, experiencing stress for that same amount of time before she's rendered unconscious and doesn't know what's going on anymore. I'm not saying one way is better than another or anything like that. Just that it seems like the stunning process is just one more step. I cannot attest to the fact that meat quality is affected if they're stressed or not. I'm not sure how it would. I do know that the chickens we raise taste much better than what we can buy at the store, and that's the bottom line for me.What Tyson does or does not do processing their birds is up to them and the USDA.
If you want to use a hatchet, a guillotine, a pair of pruning shears, or what ever method you want as far as I'm concerned it is your choice and I don't have a problem with it.
With that said, here is my position. If I am going to go to the trouble of raising a bird I want the technique used to dispatch the bird to be as stress free as possible to the bird, as it is my understanding that if you kill a bird that is stressed then the meat quality will suffer. I don't know for sure if there is any difference between taking a bird out of a cage slipping it quickly into a cone and slitting it's throat quickly induces enough stress to cause a stress problem with the meat, but if it did, then I can see that if you could stun the bird (rendering the bird unconscious) before killing him then that might very well be worth the effort.