I think that we would benefit from having a distinct legal category between man and animals. A chimpanzee has no more legal rights than a cow, despite the great distance between them with regard to sentience.
Just as the Romans had the socii*, allies who had some rights, but were not Roman citizens, I think that we should grant such a status to those animal species, and perhaps even individuals from non-socius species, which have demonstrated great intelligence and feeling. Obviously they would not have human rights, which they would be unable to exercise, anyway, but they should have some protections legally granted to them.
How great and what exactly these protections would be, I confess, I have not greatly thought about. At the very least, though, species like chimpanzees and dolphins should be protected from mankind’s excesses and given a chance to thrive and grow. Additionally, this would provide a useful framework for when or if artificial intelligences are developed.
*This word is the origin of the English word “social,” which is why a war between Rome and its allies during the first century BCE is called the Social War. The name confused me quite a bit until I learnt of this etymological connection.