Mr Coulston says his dogs were injured but did not require vet treatment because he treated them himself.
Mr Stewart and partner Anneke Wolterbeek laid a complaint with the council, saying Mr Coulston's dogs could not be controlled by him. But Mr Coulston claimed Thor started the fight and his dogs were only defending themselves.
In a copy of the investigation report provided to the Times-Age, the council acknowledges none of the animals has a history of trouble.
Neither owner witnessed the initial contact between the dogs but both gave differing accounts of what happened next, including the number of dogs involved.
With no witnesses to back up either side, the report concludes both owners should have been responsible for control of their dogs. The dogs involved in the fight will be classified as menacing by deed and must be muzzled when in public.
However, Mr Stewart said they would be appealing the classification as Thor had never attacked anyone or any animals.
"We will contest the matter through the proper channels. Thor has never bitten anybody ever in his life.
"He is not a menace and he's not dangerous. We feel the council is being too PC. Thor won't be wearing a muzzle because he doesn't need to wear one," he said.
The owners have 14 days to appeal the ruling and must put a muzzle on these dogs every time they are in public until the classification is removed.
Mr Coulston said he thought the council's decision was appropriate and balanced.
"It's such a good idea and won't be a problem for me. I think it is a fair outcome by the council," he said.
He feels his dogs wearing muzzles is added security for him and his working animals.
"It's protection as much for me as the dogs. If they are wearing a muzzle and get attacked, my dogs are not to blame," he said.
Manager environment and planning Sue Southey said such rulings were "very much for the protection of the dog".
