Against. Death is an easy out for many of the people who get sentenced. They have nothing to lose.
Another aspect that people may not have considered is wrongful conviction. It has happened before. Well guess what; you can't apologize to a dead man. Hell it's bad enough to send someone to prison wrongfully, but execute them? There is no going back when you sentence someone to death. Besides, I think it is an archaic system existing in a modern world.
It isn't just about what the suspect deserves, either. I know what a lot of people will say; putting these killers/rapists etc in jail (when they don't deserve to live) and wasting tax dollars to keep them alive is a bunch of bullshit. I say it doesn't matter; USA pretty much has a Corporate prison system anyway.
Want a better method? A better area for your tax dollars? Preventative and restorative justice. Invest in the future by spending money now to prevent crime, so you don't pay in lives or money down the road.