The loss of the life is the same, whether it is in cold blood, or in repayment, whether out of vengeance or through Capital Punishment. One other thing that should be considered is this. Most men and women on death row have some sort of friend or penpal. When someone is executed by the State that friend or penpal is victimized by the act of execution. The pain that is felt is the same as if it was their own family member.
People tend to bond to one another in all sort of relationships.
Because of this bonding it is natural for pain to occur when their friend or loved one dies, either naturally or unnaturally. Just ask anyone who has been a penpal for someone on death row that was executed. They will tell you straight up that the death penalty is wrong. Our Leaders use it to get votes. If you find yourself trapped in the system that we have, you will discover that the wheels of justice shows no mercy whatsoever.