One of the primary advantages of stone castles is they could be built taller than other types of castles. The sturdy foundation allowed taller walls that couldn't easily be breached by enemies climbing over the walls or by firing arrow volleys. The height also gave the watchmen a better view of the surrounding land. If an enemy tried to approach, the watchmen would see them, giving the castle's defenders time to mount a response.
With use of a catapult, enemies could launch fireballs at a wooden castle and quickly burn it to the ground. Stone castles certainly had areas that could be burned, but torching the entire thing to the ground was rarely possible. This advantage also served well for people inside the castle. In days where candles and fireplaces were the only source of light and heat after dark, the risk of fire was huge. Stone walls helped prevent any fire from spreading to the whole castle.
Unlike wood, stone doesn't rot and isn't subject to insect infestation. Built with heavy stone blocks, cemented together with mortar and impervious to the elements, stone castles lasted for centuries.
Even now when we see a stone castle in pictures or in person, it is an impressive sight. An immense castle, built tall and defended at every angle, would certainly have told the people living near the castle who was in charge. When William the Conqueror began his reign in England in 1066, he constructed stone castles to emphasize his power and permanence.