Capital punishment is revenge. One wrong does not right another. Just because capital punishment could be legal does not mean it is right, it just means it is legally wrong. The state-sponsored murder of criminals does not undo the suffering caused by the criminal, it simply makes the state a murderer. Indeed, as capital punishment is murder, when used it may be interpreted as tacit approval of murder.
A person cannot be unkilled, but they can be let out of jail. Consider the Christie Murders. Following the deaths of several women, the police interrogated a suspect (whose wife had been murdered), and got a confession from him. He was hanged. However, the murders continued. The police then prosecuted Reginald Christie; he hung too. They think they got the right person that time. The first hanged man was awarded a posthumous pardon, however he was still dead.
Notably, the movie 'In the Name of the Father', which was about the Guildford Four, describes how confessions are obtained. Confessions were obtained after police stuck a gun into the suspect's mouth while the signing of the confession was taking place; the other suspect confessed after police threatened to kill his father.
The Christie case also demonstrates how the punishment is not a deterrent - the hanging of the first man did not stop the killer. This is because crime is not a rational act. This lack of reason means that traditional concepts of discouraging a particular behaviour with punishment ("if you do that, you'll get hurt") are not effective. The irrational mind chooses when to follow logic.
30 years in jail is not a nice prospect, while the nonfeeling of death is potential bliss. Capital punishment might provide an incentive to be more brutal than ever.
Jail is expensive, however capital punishment is more expensive; the average cost is US$3m, including legal fees, materials, and therapy for jail employees (Scott Robertson, 1994).
The entire paradigm of punishing people for their actions is flawed, in that it serves merely to discourage a response. It addresses the symptom of the issue but not the cause. For this reason, the use of punishment creates more problems than it solves.
"It seems to me absurd that the law, which is the expression of public will, and despises and punishes homicide, commit one themselves, and, to discourage citizens from committing assassinations, order public assassination." -- Cesare Beccaria, 1764