Precisely. The worst road to go down is to confuse justice with vengeance. In this we separate justice in society from justice in the individual. We also separate justice (the notion) from law (the process).
The greater argument for capital punishment, or at least the most logical, is the notion of deterrence. Unfortunately, this doesnt work, particularly at the level of crime where the greatest support for capital punishment exists- treason, drug lords, etc. Those involved in these actions live their lives under a death sentence in their professions. A government rope isnt going to scare them.