The death penalty is arguably a less harsh punishment than a life term without parole. It can be argued that a person who knows that they have to spend the rest of their lives imprisoned is worse off than a person who knows that they will be executed after a few years in prison. The hopelessness of a life in prison could be worse than the knowledge of imminent death. In that way, one can say that life in prison is a harsher punishment and therefore more satisfying than the death penalty.
One can argue that the death penalty is better because it is more just. It is unpleasant for the family of the murder victim to have to know that the killer is still alive. The murderer may be suffering, but they are still alive and most people feel that any life is better than being dead.