Both cool mist and warm mist humidifiers are very effective at humidifying the air the same and there's not really too much difference in the humidifying level that they put out.
The humidity in the air from either a cool or warm mist humidifier are the same temperature when it reaches your lungs so they're equally effective.
However cool mist humidifiers are usually safer for kids rooms because they won't get burnt if they get too close to the humidifier.
But other than that cool and warm mist humidifiers put out the same amount of humidity and really neither is better than the other except the cool mist is the safer options for kids rooms.