Under current laws, companion animals are considered property. On the other hand, corporations have protections under a limited amount of personhood. Animals, as sentient beings deserve some fundamental rights. They do not need all the rights of a competent, adult, human being. However, they could have the right to life granted to them. This would mean that if someone murders a dog, for example if your neighbor shoots your dog for going onto his/her territory, the neighbor has violated a fundamental right of the animal. (Under current law the neighbor can be charged with destruction of property). Granting animals limited personhood and giving them some fundamental rights, will bring harsher punishments for people who violate these rights.
For example, there are no laws concerning the temperature in which dogs MUST be brought inside. It is currently a frigid January night with windchill at -3 degrees F and snowing. My neighbor has his dog outside locked in a dog crate. I think most people would find this an act of cruelty. However, because the dog does not have a fundamental right to proper shelter, this is legal. I would like to close this loophole.