I suspect that the death penalty is different from incarceration however - in that I truly believe it doesn't have much deterrent effect at all.
In areas where you have gang violence and the like - why be scared of execution your chances of being killed is so high to begin with that if anything sitting on death row increases your life expectancy.
For the suburb case there are basically three common motives for murder.
Crimes of passion: by definition these cannot be deterred, a crime of passion is an emotional act done in the moment, it doesn't include any rational thought - if it had, it wouldn't be a crime of passion, so since there is no rational consideration, there is no deterrence for it.
Crimes of insanity: again, a crazy person isn't thinking rationally, since their acts are not rationally considered, no rational consideration can deter them.
Crimes of greed: the guy who murders out of greed did make a rational decision - but he also believes he will get away with it (nobody murders out of greed if he expects to get caught) - so the punishment isn't a deterrent as he strongly expects never to experience it.
It's unlikely the death penalty has any deterrent effect whatsoever. I'm still not sure incarceration does - though like I said in the original post, it obviously reduces your odds of committing the crime again if only by making it impossible for a while.
Comparing crime rates across countries is never a very useful comparison (just look at every gun control debate) as there are simply too many factors (socio-economic, environmental etc.) which influence crime rates but are not being factored in for, but a more useful comparison is to look at countries where the death penalty was banned - and see how crime rates before and after compared.
The answer in every country I know about is - immediately before and after they were the same, over the longer term crime rates declined, but only by the same rate they were declining before.
So the conclusion appears to be that banning the death penalty had no impact whatsoever on crime rates anywhere it's been done.
Interestingly - here in South Africa the death penalty was banned in 1994. At the time South Africa had the highest crime rate in the world (a murder every 17 seconds). It declined rapidly over the next few years, but this is likely because so much of that crime was political in nature and the politcal environment had changed. Since 2000 there has been a steady decline (while the crime rate is still unacceptably high we are nowhere near the top of the list anymore) - yet calls to reinstate the death penalty remain incredibly popular among the population, one of the few things South Africans of all races actually agree on.
Personally I'm opposed to it, but I find it interesting that it's such a popular concept despite the fact that it very obviously had no impact on crime rates at all - yet it's deterrent effect is the most commonly cited reason for bringing it back. Which proves, I suppose, that what we consider "common sense" will trump facts and evidence every time.