My Jenday Conure taught me a lot about himself and parrots, so I confidently brought home my Moluccan Cockatoo. He was so different from my Conure. Some Cockatoo differences are subtler than my writing makes them appear. I exaggerate the tendencies to help make you aware of them. Some Cockatoos are not destructive and other Cockatoos are obedient, contrary to the tendencies identified here.
Cockatoos are the only parrots with crests.
Crests are used to help them express their thoughts and communicate with their flock and with us as extended flock members. The dust sometimes irritates allergy prone folks. A Cockatoo bite is said to be worse than any other parrot's as their lower beak has 2 points, resulting in a 3-point bite if delivered. Cockatoos scream very loudly. Be sure all members of your family are willing to tolerate the twice a day scream of the Cockatoo.