It is not that those other characteristics are not here. The thing is that Cloud's screentime in Advent Children and Kingdom Hearts is not stretched to that of a 50 hour RPG where he is the main character. That is the reason why characters like him and Aerith might appear a bit one-dimensional in such situations and then seem to be "reduced" to the depressed guy and the most cheerful woman ever even though they very well have their other sides. You cannot focus too much on a multi-facetted character in such a short time so you choose to use some more relevant characteristics and/or the very obvious/well known ones. Just as Sephiroth gets the "superhuman arrogant white-haired black-clothed" villain treatment in such situations even though he is way more, especially a man whose human pride has been much harmed by Cloud, a mere blue ShinRa guard, making his grudge be such an essential part of his being that it is one of his main drives nowadays.