How do they compare to other common house pets?
Measuring animal intelligence is extremely tricky. We have to use various types of proxies, like memory capability, problem solving, understanding cause and effect relationships etc. Maybe some of them just "don't care". Imagine a test that requires visual recognition: a crow might do better than a dog, but that might be because a crow relies more on sight for sensory input, where a dog maybe uses smell and hearing proportionally more. Bear in mind many household and farmyard animals, some birds, can outperform human children up to about 7 in many of these cognitive tests, but they also clearly aren't capable of sorts of intellectual accomplishment 7-year-old children are, so big pinches of salt are required.
Cats appear to have pretty good memories, but weak understanding of cause and effect, pretty bad at problem solving, and seem to be very hard to teach and train. By and large, they're worse than dogs in these categories (and rats in some). On the other hand, cats seem to show more initiative and intuition than dogs. This perhaps makes sense when we consider cats are more solitary hunters where dogs are pack animals.
I doubt you'll find many reputable animal behaviorists attempting to clearly rank animal intelligence because comparison is so difficult. What seems safe is that primates are superior to most animals. After that, gets much less clear. Elephants, dolphins (and whales?) are usually regarded a cut above. Then we're into the mass of many mammals - pigs, cats, dogs, etc. plus also some birds (e.g. crows), and octopuses. Some have argued octopuses might be about as or even more intelligent than elephants, but they're particularly hard to compare as they're just so different.