I generally support the concept of the death penalty, but most states use it so rarely that it's irrelevant. And when they do, there are so many appeals that it may take decades. The inmates often die of natural causes first.
In terms of punishment, it depends on where the convicted is coming from. A friend in the FBI tells me that many of the Russian immigrants that he prosecutes in RICO cases laugh at our prison system. They call it "The Hotel" It's hardy a punishment for them. A good friend of mine is a CO in A block at Sing Sing. That's the largest cell block in the US. The inmates there are not scared of prison either. For some of them it's an improvement over where they came from. Three meals a day...Air Conditioning in the summer, weight rooms, basketball courts. They are surrounded by constant prison violence. But they were surrounded by that before they went into the system. The only guys who are really heavily punished are the ones in what they call "The Shoe". They are in 23 hour lock down for behavior problems in the system.
On the other hand, as an example...if you are a dentist from a wealthy backround convicted of killing your wife...Prison will be utter hell for you. In that case you'd probably crave the death penalty. The severity of the punishment is a matter of where you come from.
I generally don't see the death penalty as a deterrent. I just simply support it, because I don't want the taxpayers to pick up the bill in perpetuity for the worst of the worst. The cost of death row would be a lot less if we didn't have an endless appeals process.