An article in The Conversation explores the variety of neuron structures in the elephant brain.

Taken together, these morphological characteristics suggest that neurons in the elephant cortex may synthesize a wider variety of input than the cortical neurons in other mammals.

In terms of cognition, my colleagues and I believe that the integrative cortical circuitry in the elephant supports the idea that they are essentially contemplative animals. Primate brains, by comparison, seem specialized for rapid decision-making and quick reactions to environmental stimuli.