I agree excessive panting is a sign of stress they need to see a vet it could also signal something more serious if this is new and start all the sudden it could be anything like (heart worm, chf) Bottom line if this is new and started suddenly they need a trip to the vet office to get a examination, i would not wait.
Well it sounds like you have two of them panting very confusing.
Anyway consistant panting is a sign of pain or stress.The best thing you can do is take them/him to the Vet if he goes off his food as well.