I always felt that life imprisonment would be more painful, in total, than a quick death. Then you account for all the appeals and structure of the execution itself costing about as much as supporting the prisoner for XX years, so economically it's a wash. And then there's the risk of executing someone on bad evidence or whatever and you would have exonerated them later - which you can do with imprisonment until dead but can't do with hanging until dead. Finally, knowing that we as a culture are able to practice restraint, to not give in to base instincts of revenge-killing, adds some cultural pride. And you want the neutral historian who investigates later to find that your side was in the right, rather than everyone just being shitty to each other.
While you may not agree with those things, and there are probably arguments for the death penalty, I personally am against it.
Then again, if you have a guy who just can't be kept in jail, but who would otherwise be kept in jail until dead - you have a choice between locking him up so well that he can't escape but leaving him in inhumane living conditions (underground, chained to floor, and in isolation), or just killing him. There's a point where you have to ramp up the penalty rather than let him run around free. It's the same as someone in minimum-security prison who keeps escaping: you need to stick him in a less-humane, higher-security facility.