The difference can be seen even when the amount of brain cell death is the same in both groups.
Study leader Robert Perneczky, from the Technical University of Munich in Germany, said: "These results add weight to the theory of brain reserve, or the individual capacity to withstand changes in the brain.
"Our findings also underline the importance of optimal brain development early in life, since the brain reaches 93% of its final size at age six."
Head size is one way to measure brain reserve and growth, he said.
While brain growth is partly determined by genetics, it is also influenced by diet, infections and inflammation.
"Improving prenatal and early-life conditions could significantly increase brain reserve, which could have an impact on the risk of developing Alzheimer's or the severity of symptoms of the disease," said Dr Perneczky.
The researchers looked at 270 people with Alzheimer's who underwent tests of memory and thinking skills. They were also given magnetic resonance imaging scans to assess their levels of brain cell death.
Measurements were taken of the circumference of patients' heads to determine head size.
The results, published in the journal Neurology, showed that having a big head was associated with better test performance despite brain cells dying off because of Alzheimer's.
Specifically, for every 1% of brain cell death, an additional centimetre of head size was linked to a 6% improvement in a person's memory.