Final answer:
Alteration of consciousness is the sign that best differentiates between delirium and dementia, with delirium exhibiting a sudden change in consciousness while dementia involves a gradual cognitive decline.
Step-by-step explanation:
The sign that best differentiates between delirium and dementia is E. Alteration of consciousness. Delirium is typically characterized by a sudden change in consciousness and cognition, which can include confusion, disorientation, and disturbances in the sleep-wake cycle. On the other hand, dementia is more of a gradual decline in cognitive function and usually presents with symptoms such as disruptive memory loss, confusion about time or place, and difficulty with planning and executing tasks. While both conditions may share some symptoms like confusion and disorientation, dementia patients tend to maintain their level of consciousness, whereas delirium involves a fluctuating level of consciousness.