From Wikipedia:
The largest brains are those of sperm whales, weighing about 8 kg (18 lb). An elephant's brain weighs just over 5 kg (11 lb), a bottlenose dolphin's 1.5 to 1.7 kg (3.3 to 3.7 lb), whereas a human brain is around 1.3 to 1.5 kg (2.9 to 3.3 lb).
And a cow has a brain one hundred times great than that of a mouse, but is it any smarter? Or a honeybee with a brain weighing a milligram has the ability to navigate as well as many mammals.
Elephant brains have three times the number of neurons found in the human brain(257 billion to our average of 86 billion), but 98% of them are packed into the elephant cerebellum. On the other hand, an elephant's cerebral cortex, which is twice as big as ours, has only one third the number of neurons found in our cerebral cortex.
I hope I don't bore you too much with the following, but ornithology is one of my interests:
Plenty of bird species(not all) show evidence of complex behaviour, including counting and categorising objects.(African grey parrot, pigeon). Erich Jarvis(a neurobiologist) suggested the following:
'About 75% of our forebrain is cortex, and the same is true for birds, particularly species of songbirds and parrots. They have as much cortex, relatively speaking, as we do. It's just not organised the way ours is.'
And the cells show similar characteristics(e.g. chemical neurotransmitters, nerve circuits). It seems that the connections between brain cells are vital for complexity of behaviour.
In 2014 neuroscientist Suzana Herculano-Houzel(that's a mouthful) and her colleagues determined the number of neurons and other cells in the brains of a variety of parrot and songbird species. They found, in her words, that they 'pack surprisingly high numbers of neurons, really high, with densities at least akin to what we find in primates.' And the above lady's team found that nearly 80% of a macaw's brain neurons, for instance, are contained within the cortexlike part of the brain, while only 20% reside in the cerebellum. This is very much the opposite of the ratio found in most mammals such as the elephant.
All of which suggests that, although the ratio of brain size to physical size may well be important, the detailed evidence of how an individual species' brain is constructed plays a much greater part in a species' complexity and behaviour.