Depends on which animal you mean. The very basic instincts of an insect or a crab can´t be compared to highly intelligent animals such as dolphins or simians (higher apes). The whole issue of cognitive intelligence goes up on a very gradual scale from primitive life forms right up to humans. Gorillas, for example, (and I believe chimps too) have been taught sign language and are able to communicate and indicate a great deal of awareness of not only their surroundings, but even their identity. Some simians have shown IQs of around 80, which surpasses some humans. Check out Koko (links below) as an example; she communicates, expresses emotions, paints, etc. - I see no reason personally to say that she has no "soul" whereas any barbaric, sadistic and mentally underdeveloped human has. As for genetics that you mention, gorillas and chimps generally share around 97-98% of same DNA as us humans, so there isn´t much difference there.
about Koko: http://www.koko.org/