It doesn't really matter. Different people are more terrified by different things. Some fear imprisonment more than death. For others it is the opposite. I bet there are many who are in the situation that don't see much of a difference. If people are not going to be rehabilitated, I see no point for life in prison over death. Since I do not believe in punishment for revenge, I see no benefit of death penalty over life imprisonment. And both are unpleasant ideas that should deter rational people.
The problems are:
1) Some people are just irrational, possibly in need of psychiatric help.
2) When your life is pure **** anyway, the incentive to avoid prison is lessened by a great deal.
3) If your experience and knowledge base convince you that you will never get caught, fear will not deter you from a crime
4) If you think you are going to die anyway, as many in gang-plagued areas do, fear of death will not deter you from crime.
5)Even normally rational people are a lot less rational at the time a capital crime is committed.

Explain how the death penalty would change this. People like you and I (well, I assume you) would probably not kill even if there was no law against it due to upbringing, empathy, and a knowledge base suggesting that killing won't do us any good, as well as a general distaste for death (from upbringing and possibly influenced a bit by biology). The death penalty makes little difference for us as well.

So better law enforcement and better living conditions and better upbringing are real solutions. The death penalty is just one of those dumb issues people argue back and forth about to no avail.