Diverse Dogs and Familiar Felines
Even with cat breeds as distinctive as the sphynx, there's no solid argument that can be made that dog breeds are more diverse. From coats to size to skeletal structure, there is a far wider range of traits displayed among dogs. And it is a curious thing to wonder at. After all, both domesticated cats and domesticated dogs all fall under the umbrella of one species: Felis catus and Canine familiaris. Why should one be more diverse than the other? In fact, why should either species be as diverse as it is at all, with members who vary so greatly in appearance?
The answer to the second question is quite simple: selective breeding. Just as farmers have selected cattle and refined them for either their milk or meat producing traits, so have we selected to favor certain traits over others in our pets. For example, the sphynx cat was simply a genetic mutation that happened somewhere to some cats in the 1970s, offspring produced by completely furred cats. It was decided that it was a favorable trait, and hairless cats were selected to breed with other cats until there was enough diversity to establish a population of hairless felines breeding only with other hairless felines. Several generations later the cat breed we now recognize as sphynx was established.
As for why there's a different level of variety between dog breeds and cat breeds, it comes down to two factors: time and purpose. Dogs have been domesticated for over ten thousand years, as compared to the far more recently domesticated cats who joined our companionship, instead of just sharing the outdoor parts of our inhabited areas, a mere three thousand or so years ago. And we elected dogs to be our companions. We invited them to be part of our pack, and incorporated them into our lives with intention. We used dogs to hunt with, to guard our dominions, and to herd, along with many other tasks as years wore to generations. Dogs had a crafted purpose. When we wanted to protect dogs from getting brained by an objectionable cow, we bred for thicker skulls, shorter legs, or a faster run. When we wanted them to guard our homes we selected those who were especially loyal and territorial. And when we wanted them to hunt we selected for the best noses and ears. There was purpose behind the decisions we made. Utilitarian purpose. For better or for worse, though now that most of that purpose has mellowed, issues with selection and inbreeding are becoming increasingly commonplace. Though it is being addressed we collectively recognize the problem. Cats were already perfectly designed for their task and performed it without our request. They hunted the rodents and we let them co-habitate our settlements. It wasn't really until we started taking them in as "inside" pets that we started to define different breeds for ourselves. Most of which are selected for appearance rather than a drive for some practical end.
Different timelines, different reasons, and either way, we still have a dizzying selection of wonderful companions.