It is generally an advantage for plants to stand upright and grow as tall as possible. Plants need sunlight, so growing taller than neighboring plants make it more likely that the plant will survive and successfully reproduce. For animals, height may be an advantage sometimes as well, but most animals have skeletons and musculature. They do not need the rigid network that cell walls provide to stand upright.
Furthermore, most animals can move, and this capability is an enormous advantage when it comes to feeding, finding a mate and escaping from predators.
