No, dogs and cats experience pain VERY different than chickens.. To give you an example;
My dog was bit by another dog once, and needed seven staples. She was clearly in pain, shaking, whining, refusing to move, showing teeth at dogs that came close. The wounds were not even bleeding much, they just clearly hurt a LOT.
One of my chickens decided to tease one of my dogs by trying to peck at her. She responded by ripping a bunch of skin and feathers away from it's chest. The chicken squealed until it was let go (and by that I mean until the skin came away) and five minutes later showed no sign of the fact that it had a gaping open wound on it's chest. I isolated it and treated with warm water and iodine. It freaked out until I gave it a buddy to keep it company; it was more upset about being alone then ripped open by a dog. I looked at the wound today, and it's a good 2" square on a bird only 2lbs.
It'd be like having the whole top left quarter of your chest skin ripped off but the bird did NOT care!
The conclusion? It's just not the same. This bird is and has been since 5 minutes after having 1/4 of it's chest ripped off acting completely normal. It was still bleeding while running in circles to ask for food and leaping up on it's box to try to fly out of the cage, etc. with 1/4 of it's chest skin missing. It's now well on the mend, missing 1/4 of it's chest skin with nothing but 10% iodine, warm water and a clean environment. The bird is healthy as any of the others I have, you could not pick it out of a crowd.
With this in mind, if you get good at caponizing there's no reason it wouldn't be a fairly stress-free and nearly painless, easily recovered from operation for a roo to be caponized. It can't be worse than having 1/4 of your chest ripped off and that doesn't seem to phase chickens at all apparently!