First of all, it depends on where and how extensive the injury is. Second, it depends on the age of the person and general health status at the time of the injury. There are many other factors, such as general health history, history perhaps of substance and alcohol abuse, nutritional status, and to some extent, genetic makeup that all determine outcome and prognosis of brain injury. The answer to that is one of the most exciting areas now being investigated, and it's an important one. Females obviously respond to medication differently, in many cases, than males do.
Critical data seems to suggest that females recover better from brain damage than males.
But this may depend on where they are in their hormonal cycle at the time they have the injury. If they're high in progesterone at the time of the injury, the outcome is better than if the same kind of damage occurs when the female is high in estrogen. This relationship calls a number of different types of traumatic brain injuries, such as stroke, penetrating injuries, and even damage to the spinal cord. Recently, I just saw a paper showing that pregnant female laboratory rats learn complex tasks better than when the pregnancy is over. The investigators reported that the better performance is correlated with higher levels of progesterone in the brain.