The correct answer is neither is more “Stoic” than the other. For one thing, they do not follow the philosophy of Zeno of Citium. However, they both live approximately in agreement with nature. Also, living in agreement with nature for a cat is very different than living in agreement with nature for a dog.
The question is how much does your individual cat or dog live in agreement with nature? For a human to live in agreement with nature, they have to mature emotionally and rationally to their full potential. Essentially, no one really completes their full potentiality because if they did, they’d be a Sage. So the same probably goes for cats and dogs. Does a cat or a dog ever really mature fully into their full potential? Maybe a few but they’d be rarer than a phoenix.
What does it mean for a cat to live up to its full potential as a cat? Well, perhaps it would have to be very good apex predator. It would need to be able to catch mice really well. It would need to take plenty of catnaps. It would need eat the right amount and clean its coat sufficiently. It might need to produce the requisite amount of hairballs. Perhaps if you saw that cat, you’d be like, “well, that’s definitely a cat!”
What does it mean for a dog to live up to its full potential as a dog? Well, perhaps it would need to be appropriately loyal to its human. If it was a feral dog, maybe it would need to be part of a pack and maybe even do the appropriate things as a pack animal. Perhaps it would be really good at following the lead dog or if it was a lead dog of the pack it would be really good at leading. Maybe if a human called it “a good boy” it would take that as an initiative to be a good boy. A “good” dog certainly would be very trainable.
So that’s the definitive answer. Cats and dogs are not really any better than the other with regard to Stoicism. Cats will be cats and dogs will be dogs. Some dogs are better at being dogs than others. Just like some cats are better than other cats at being cats. Can anything ever really live in agreement with nature? Not when taken apart. But when looking at the whole nature definitely lives in agreement with itself.