A monster on a par with human's intellectually would be a formidable foe indeed. But the monsters are stronger than humans and have many characteristics that let them dominate the average human, until a hero comes along and saves the day by conquering the monster. The most poweful and near invincible monsters cannot be defeated by humans alone, but require help from the immortal gods. Monsters have specific powers also, but these vary. They range from the Hydra's ability to regrow its heads, to the Gorgons turning those that gaze upon them to stone.
Some monsters are fantastic in size, while others are murderous maniacs.
Appearance usually indicates in what is and isn't a monster. If a figure is human-looking, no matter if he is insane and blood thirsty, most people would not consider him a monster, while a hideous beings even if he is good natured and kind, would be considered a monster by many. Monsters rarely act by themselves, but are used by a power greater than they are, usually fate or a god.