Is the death penalty better retribution?

As an admirer of C. S. Lewis's essay on the Humanitarian Theory of Punishment, I nevertheless have reservations about the retributive adequacy of the death penalty.  I guess the question is whether the death penalty is better retribution than, say, life without parole. I think that people make a mistake when they think that a penalty fits the crime better if it resembles the crime. If we want resemblance to the crime, our current methods of execution give the criminal a painless death which the criminal denied to  his victim. But torturing a murderer to death is cruel and unusual punishment.