I don't think it's so much the ability to make a character "scary", in this case, the reality is, overally, Godzilla is an offensive creature, King Kong is a defensive creature.
In '33, '76 and 2005, every Kong story has outside man entering Kong's world and disturbing it, his only acts of aggression towards men to defend against the invaders. Then he's taken from his world and dropped into one he doesn't understand and in trying to cope, is attacked by man. On top of that, Kong is very mortal and affected by our weapons.
Godzilla is a beast that invades man's world. He destroys our world with no reason and he's almost immortal.
The nature of Godzilla allows for any number of stories to revolve around him and depictions of him. For better or worse, even when physically depicted as more a Hollywood creation than zoo animal, Kong was created as an animal, to be true to what he is and not be something other than Kong is to be bound by heavy limitations, hence why so few films have been made using him.
I love Kong movies, don't get me wrong, I own all 3 origin films and King Kong Lives, the only ones I don't care for are the Toho films outside of Kong vs Godzilla, but he's a very unique monster in the larger universe of movie monsters, more akin to the shark of JAWS than Godzilla.