As a pet owner, you should consciously choose between the covered and uncovered models of the litter box. Cat behavior experts say that not all cats have the same temperament. Some are shy and may feel inhibited to litter openly. They might like a discreet littering space. On the other hand, some cats are more of extroverts and may prefer to litter in an open environment.
For this reason, the decision should be based on your cat's temperament. The key consideration should be that your kitty should feel comfortable and at ease in the litter box.