You actually need both.
Think of your brain as the sound deck and the soul as the music, on CD or whatever. You won’t hear a note unless you have both the content and the hardware. Likewise, your mind (which “personality” is the expressive surface of), will, and feeling are part of your soul. But they need the brain, and by extension the whole human body, to live and express life. Without a working head and body, there is no thought, no feeling and no action to be willed.
Animals do have a soul; that is why we call them animals (‘anima’ = ‘soul’ in Latin). Theologically, it is said that the souls of animals are not sustained after death. Not sure why. Because they have a soul, they have the propensities of one, but not the cognitive mind, which comes with a human soul.
After you pass through death, in eternity your Spiritual Body will take over the task of holding and expressing life in your soul, which before death is done by your “Human Body”.
ICXC NIKA.