Summary: I estimate, for humans and the most common domestic land animal livestock populations, their absolute and relative contributions to the total brain mass of the combined category. Humans make up the vast majority of the aggregate of brain mass for these populations, followed by cows. Chickens account for less than 1% of the total neural tissue of humans and domestic land animal livestock. As a proportion of the total number of neurons across these populations, cows and chickens are closer, due to the relatively high neuron density of chickens and humans, while the human proportion is higher.
 

AnimalGlobal populationBrain mass (g)Total grams of nervous system% of human and farmed land animal brain mass
Human7,110,521,2931,3509,599,203,745,55090.23%
Chicken20,708,002,000482,832,008,0000.78%
Sheep1,093,566,764140153,099,346,9601.44%
Pig967,164,630180174,089,633,4001.64%
Cow1,426,389,031442629,750,757,1875.92%
Total31,305,643,718-10,638,975,491,097100%

 

This post does not address farmed marine animals, because data quality and conceptual issues are less clear than for land animals (the role  of wild-caught fish, etc), although I may address that at a later time. Population figures come from the UN Food and Agriculture Organization and are from 2011.

At the time of this posting the United States Census Bureau World Population Clock gave an estimate of the world human population at 7,110,521,293.

For brain mass, this table provides numbers for humans, cows, sheep, and pigs (where a range is given, I take the midpoint). For chickens, Rekhamper et al. (2002) provides brain masses for 8 breeds of chickens, ranging from 2.6 g to 4.4 g, and I use 4 g in the table.

ETA:

Neuroscientist Suzana Herculano-Houzel has performed numerous studies to determine neuron count in various species, and argues that neuron count better tracks cognitive abilities than brain size. She provides an estimate of 85 billion neurons for a human brain, and 221 million neurons for the Red Junglefowl, a wild relative of domesticated chickens. She also studies scaling patterns of brain size and neuron count in various taxonomic groupings, and in her book estimates that a cow would have ~3 billion neurons.

A neuron-count with these estimates would have almost no effect on the relative proportion of chickens, but would reduce focus on cows to on a par with chickens.

AnimalPopulationSource of EstimateNeuronsTotal Neurons% of neurons in human population
Human7,110,521,293.00Isotopic fractionator85,000,000,000.00604,394,309,905,000,000,000.00100%
Cow1,426,389,031.00Herculano-Houzel projection in The Human Advantage3,000,000,000.004,279,167,093,000,000,000.000.71%
Chicken20,708,002,000.00Red Junglefowl221,000,000.004,576,468,442,000,000,000.000.76%

Wild invertebrates, rather than humans or farmed animals, account for the vast majority of neurons on Earth.

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