This is funny. The word personality has as root meaning an actors mask. This is a hint that there is something fake and artificial going on, and not indicative as having spiritual implication.
I think that elaborated distinction among human beings arises through dualistic thinking and categorizing. So yes, depending on how you want to look, you can find probably more refinement in characters among humans, than among an other animal group. But this is only at a superficial, conceptual level, and not in reality. You can see humans as easily as being all just the same. Viewed in the second way, humans wouldn't have unique/individual souls or spirits. Notice that humans not only use this to create distinction between humans and animals, but also between human groups internally as well...
Are all beings the same, or all different? I do hope that all beings have a unique spirit/soul and are not at the deepest level all the same as for example Hinduism beliefs. I don't like about 85% of the human beings (NB nothing to do with race, religeon, class, or nationality etc.), and the very thought of being the same as them makes me sick.
In short, animals have distict characters (unique spirits, souls, personalities) from one to another, but not as easy to see as in humans.
I hope this is a clear answer to your question.
