I'm Catholic, and I'm almost always against the death penalty. The death penalty is only for the very gravest situations if there is not possibly another way to protect innocent life. However, in a country as great as ours, we have numerous ways of ensuring that the bad guys don't get out again. Solitary confinement is an example. I think that the death penalty is used way too often, when a better solution exists. Human life is too precious to me to be taken lightly.
To answer the "eye for an eye, a tooth for a tooth," quote the Bible, Matthew 5:38-48. Sure, you have to defend yourself and others, but at the same time you have to know where to draw the line. You don't want to be merciless. If they abused children, does that give you the right to abuse them in the same way? No. To stoop to their levels of hatred just to "show them how it feels" is wrong. That has now turned to revenge.
To quote from the Catechism of the Catholic Church: "Assuming that the guilty party’s identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.
If, however, non-lethal means are sufficient to defend and protect people’s safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity with the dignity of the human person.
Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm—without definitively taking away from him the possibility of redeeming himself—the cases in which the execution of the offender is an absolute necessity are very rare, if not practically nonexistent." (CCC 2267)
Hope this helps!