We tend to argue this, as we argue other things, one a case-by-case basis, almost ad hominem. (I have no single case in mind here. This is a composite of cases I know of.)

Consider it this way instead: if someone is convicted of serial murder -- and I mean that the his fingerprints and DNA were found on the bodies, on the axe the dead were chopped up with, in the garage where the chopping was done, on the videotapes he made when he was doing the killing, on the clothing of the victims, and on the plates and utensils he ate parts of his victims with -- would the greatest good for society be served by his execution or by letting him live out his life in prison?

In prison, there is the possibility of escape or even release. With execution, there is no hope of studying him, of finding out what made him the way he became. With execution, there is also no possibility of him repeating horrific crimes.

Don't consider vengenance or "closure" in your answer -- look only to serving the greatest good for society.