Scientists at Vanderbilt have released the first scientific study to actually count the number of cortical neurons in the brains of a number of carnivores, including cats and dogs.

Bottom line: Dogs have about twice as many grey cells associated with thinking, planning and complex behavior as cats. Dogs have about 530 million cortical neurons, cats have about 250 million; humans by comparison have 16 billion. 

According to Associate Professor of Psychology and Biological Sciences Suzana Herculano-Houzel "our findings mean to me that dogs have the biological capability of doing much more complex and flexible things with their lives than cats can. At the least, we now have some biology that people can factor into their discussions about who’s smarter, cats or dogs."

Good news for raccoons, they have as many cortical neurons as dogs in a brain the size of a cat.

https://news.vanderbilt.edu/2017/11/29/grumpy-cat-study-dogs/

The paper is here: https://www.frontiersin.org/articles/10.3389/fnana.2017.00118/abstract