Sometimes. But not usually. I know many people on Death Row, and most of them are decidedly repentant and not evidently psychopathic. Here in Georgia, the difference between getting the death penalty and getting a life sentence is largely a matter of jurisdiction. Killers from the bigger cities, especially Atlanta, are very unlikely to face capital punishment. Killers from rural areas are far more likely to be considered for the death sentence. There is no apparent difference in the severity of the crimes or the attitude of the criminals.
Then perhaps you could explain Richard Ramirez. Or Resendiz. Or this Duncan fellow. Or how about the bastard who killed Jessica Lunsford?