A reading of the dictionary definitions of the words justice and vengeance reveals why there is so much variety of opinion on this subject. It becomes clear that we have no objective standards by which to make a distinction between justice and revenge, and the two become equated. Our opinions are charged with emotion, thus are subjective. It seems that we will never have a consensus with regard to the state executing a criminal (so-called capital punishment) unless we can evolve beyond the primitive desire for revenge.
What does vengeance accomplish? If you steal from me, and I find a way to steal from you, how does this help either of us? If you rape and kill my daughter, how does it help me, or society, for the state to kill you? Must we become executioners ourselves in our attempt to satisfy our illusion that this will make things better? Execution does not cancel out the wrong as if it has never happened. It merely appeals to our primitive desires and makes us executioners.
As for the prevention of future harm by the same perpetrator, a lifetime in jail will suffice, and we will not have set the bad example of using violence in the attempt to solve a problem.
justice: the quality of being just; righteousness; equitableness; the administering of deserved punishment or reward.
vengeance: the act of retaliation for injuries or wrongs (syn: revenge)