I think the main difference is that we can use reasoning and logic to contradict our instincts - we feel a fear response at something that is strange or different, but instead of attacking it and running away, we can rationally investigate it and conclude something based on our experience. We also have a sense of cause and effect, and through that, of time.
Animals surely have souls, and sure they think too, but I don't think it's generally beyond immediate concerns like recalling that nice little hollow they slept in or where to get the best honey (guess the animal!) Of course, that's surely not true of all animals - dolphins and bonobos and other higher primates, for example, might be as intelligent at least as we are, and simply because we equate technology with intelligence, does not mean they don't have a different higher mind.