A cat has fewer than 1 billion neurons, while a dog has 2 billion.

Judged as of 2021, interpreting the counts as cortical/brain neuron counts as commonly cited. True: published neuron counts (for example, Jardim-Messeder et al. 2017) show a cat brain or cerebral cortex with fewer than 1 billion neurons (for example, about 250 million cortical neurons) and a dog with about 2 billion (for example, about 2.25 billion cortical neurons), both measured on the same basis (cortex or whole brain). Mostly true: both figures are roughly right, but the basis is mixed (for example, cortical against whole-brain), or the dog's figure falls between about 1.5 and 2.5 billion. Mixed: one of the two figures holds and the other does not. Mostly false: both figures are off, but the ordering (dog more than cat) and the rough scale hold. False: the cat has more than 1 billion neurons on the relevant basis and the dog's figure is far from 2 billion, or the ordering is reversed.

Set before the research began.

1. E1 Dogs Have the Most Neurons, Though Not the Largest Brain: Trade-Off between Body Mass and Number of Neurons in the Cerebral Cortex of Large Carnivoran Species PubMed Central (NCBI) · 12 December 2017

   “Both dog individuals examined (a 7.45 kg mixed-breed and a 32 kg golden retriever) had larger brains than the cat (brain mass in dogs, 58.4 and 114.5 g, respectively; cat, 34.8 g), and also more brain neurons than the cat (dogs, 1.8 and 2.6 billion neurons, respectively; cat, 1.2 billion neurons).”

2. E2 Dogs Have the Most Neurons, Though Not the Largest Brain: Trade-Off between Body Mass and Number of Neurons in the Cerebral Cortex of Large Carnivoran Species PubMed Central (NCBI) · 12 December 2017

   “The same applies to the cerebral cortex of the dogs, at 46.2 g with 429 million neurons and 84.8 g with 623 million neurons, against 24.2 g with 250 million neurons in the cat.”

3. E3 Dogs Have a Lot More Neurons Than Cats Scientific American · 1 July 2018

   “A typical mutt clocks in with almost 430 million neurons in its cortex, and a cat has just 250 million.”

E2 and E3 put the cat's cerebral cortex at 250 million neurons, which supports the "less than a billion" figure for the cat. On that same cortical basis, though, dogs have about 429–623 million neurons (E2, E3), not about 2 billion. E1 gives whole-brain counts of 1.8 and 2.6 billion for the two dogs, roughly matching the "2 billion" figure, but 1.2 billion for the cat, which is over 1 billion. So both figures are roughly right only when the cat's cortical count is set against the dog's whole-brain count, which is the mixed-basis case the criteria call mostly true.