Is physical prowess more important than mental agility

No! Because you must have the mental agility to guide your physical prowess. For example, you can attack your enemy in a battle because you have superior weapons, infantry etc. But your prowess will not amount to much if you attack the opponent in the daylight and from a vulnerable position. For that, you need mental agility, or the ability to think of creative solutions to problems. Only then can you use your physical prowess to your advantage.