I voted dog, but we had both. We always had three dogs and one cat. I have a dog now, as well.
I don't remember them ever being sick, honestly. The dogs were inside / outside pets and spent most of their time outside. The cat was an inside / outside pet who spent most of her time inside. About three years ago, the cat developed and abscess at the base of her tail and had to have that treated, but I don't know what caused that (and that was shortly after I had moved out). That's the only issue I can remember, aside from them getting into things outside that just made them throw up.
ETA: Up until I was about thirteen we had a dog who had had distemper as a puppy.