You have to distinguish and differentiate between type of intelligence and the social (human or the housed community) intelligence.
Dogs orientation and behavioral dynamics have to do with being pack animals. They prospered in evolutionary process by being social animals oriented towards being around man and pleasing man. They have a social intelligence that runs parallel and connected to man. Man needed dogs (genetically connected to wolves orginally that adapted) for hunting and protection from other wild animals, so they were domesticated early.
Man and dogs prospered greatly as a result of this symbiosis.
Cats are not pack animals. They are curious about humans behaviors but don't have a human-oriented social intelligence. They were domesticated later in development of humans (away from the cave days). They operate as independent operators. Whose survival was more about their self-reliance but close or nearby to human communities.
Domestic cats can survive a week or more depending on whether feral (recently) or not. But if you left the house for a week, a dog would be much further behind than a cat given the same food and water supply.
They've different programming and nature...pack vs non-pack animals. Comparing relative intelligences involves a bit more complicated comparison criteria as you need to test them in environmental-neutral tests. Very hard to do as the testing involves interacting with man and the way they both relate to man.
A domestic cat will keep a home varmint-free. A dog, in most cases, not so much; however, a cat will not fetch, typically - unless it's a mouse you want fetched. And, when mouse is caught, the cat will stack the mouse at your feet or your doorsteps or doorway.