This argument has been going on for tens of thousands of years. Dog owners point out that dogs can be trained to hunt for us, herd our livestock and do many other tasks. Cat owners maintain that cats are too smart to take part in these menial pursuits.
Intelligence has nothing to do with the size of the brain. Whales are not smarter than humans even though Moby-Richard seemed to be smarter than Captain Ahab.
Rather the neurons in the cerebral cortex are the brain cells responsible for intelligence, thought, planning and behavior.
A study conducted at Vanderbilt University compared different animals to see how the numbers of neurons in their brains relate to the size of their brains. The researchers analyzed the brains of one or more ferret, mongoose, raccoon, cat, dog, hyena, lion and brown bear.
They found that dogs have about 530 million cortical neurons while cats have about 250 million. Human brains have 16 billion. A Golden Retriever in the study had the most cortical neurons of all the animals, with 627 million. (Demand more respect, Honey.)
The study found that raccoons had far more neurons than their small brain size would suggest which would explain some garbage can and campground mysteries.
Brown bears, on the other hand, had only as many neurons as cats, despite the obvious size difference. A.A. Milne had it right--
“When you are a Bear of Very Little Brain, and you Think of Things, you find sometimes that a Thing which seemed very Thingish inside you is quite different when it gets out into the open and has other people looking at it.”
--A.A. Milne, Winnie-the-Pooh
Any argument about their cognitive capabilities at this point will be largely a matter of opinion until direct, systematic comparisons of cognitive capacity are performed across these and other species.
Or maybe never.