Brain size varies in living beings and there is no correlation of the size of the brain and the level of intelligence. This therefore, means that finding out how the human brain is more advanced compared to other living beings with similar or larger brain sizes is of interest.
The pre-frontal cortex may hold the key, where the the number of neurons here in the human brain is far more than any other animal. The pre-frontal cortex is the area which holds the key to abstract thinking, decision making and detailed planning. There are 16 billion cortical neurons in the human brain compared to 6-7 billion in chimpanzees and 9 billion in orangutans and gorillas.
The introduction of cooking meat has allowed humans to ingest more calories from the foods collected, whereas raw fruits and vegetables would take more time to chew and digest and contain less calories. The use of tools also allows a person to spend less energy on preparation, hunting and gathering and more energy from the foods they consume.
This therefore means that our increased neurons and complexity compared to other primates may be explained by our increased intake of fats and proteins.
To read more on this subject read the book ‘Human Advantage: A New Understanding of How Our Brain Became Remarkable’ by Herculano-Houzel (2016).