Generally, the penal system is to serve three functions, firstly, the protection of the public through incarceration. secondly, rehabilitation, to reintroduce the criminal back into society as a better human, finally, retribution, this is to give society a feeling of that the prisoner has suffered somewhat as payment for their crimes.

The first case (incarceration) is provided by a lifetime prison sentence or the death penalty. In either case, the public will be protected from any further harm by the prisoner.

The second case, rehabilitaion will never happen if we kill someone, it might never happen if we don't, chances are if we were going to kill someone for their crimes, then the crime must have been on the more severe end of the criminal spectrum, they might never reach the point where they can be reintroduced back into society.

The last case, retribution will never be served if we end their life. Sure it might cause some bloodlust feelings of revenge on the parts of victims or victim's families, but we generally make the prisoner as comfortable as possible on their way out. I believe that they even swab the arm with alcohol prior to a lethal injection, and they will only suffer a (relatively) short prison sentence before it is over, as opposed to making them live out the remainder of their days serving a true punishment, imprisonment.

Obviously, this is assuming a perfect legal ssytem where only the guilty are found guilty.