I've eaten both, cat in China and dog in Korea. Both were prepared as animals raised for food, not someone's pet! Both countries have long since banned both for food but as it was such a common staple they are still found in small family restaurants everywhere in those countries, and you can find live and slaughtered cuts in larger street markets.
Dog had a much stronger flavor than cat, but both were stronger flavored than mutton. They are not something I'd go looking for for my birthday dinner, but neither was difficult to eat. The dog I've eaten several times in Korean street market stalls was always prepared as a thick spicy stew. I've only had cat once in China, and it too was a sort of stew, but with a clear stock.
It's my habit when traveling in unfamiliar parts of the world NOT to ask what I'm eating until I've finished. Otherwise I'd probably starve. I ate Fruit Bat Soup in the Caroline Islands, and I know there is no way in hell I'd have eaten it if I knew what it was! I turned down 'balut' in the Philippians as I could see it was an unhatched baby chick about a week before hatching... Raw horse meat in southern Japan (delicious,) unfertilized chicken embryos all over the world, and some folks were aghast that I would happily eat Bambi!
Stitchawl