Don't expect too much from me... Ethics never was a main topic for me.
I would say, as any sensible person, just the risk of giving capital punishment to an innocent should be reason enough to refrain from it. And AFAIK deterrence seldom works.
So I think incarceration might be the best solution, in the first place simply because we put somebody away who has proven to be dangerous, in the second place we, i.e. society must attach consequences to people who do not want to play by the rules. However, if a society does not take the chance to rehabilitate the offender, it is not much use. Just putting somebody in jail, specially when it is overfilled, you create offenders and possibly more radical ones too.
In this respect, it seems to me that there is a huge difference between prisons here in Europe, and in the USA. Most of the times rehabilitation is the aim. Therefore we might take some risks, letting out somebody who will still act criminally (which hurts extremely when its is murder on innocent people), but I think a lot more crimes are committed by ex-inmates who were radicalised by their life in prison.
To get a glimpse of the difference between the USA and Scandinavia, there is a short series about 'the Norden'. This is the episode about prisons (the others are just as interesting):
https://www.youtube.com/watch?v=HfEsz812Q1I
To get back at capital punishment: there are also examples of murderers who felt much remorse about their killing, and ended up meeting the family of the victim, or became meditators, even meditation teachers to their fellow inmates. These are pretty extreme examples of course, but just killing a criminal, or putting him/her in jail purely as punishment I find useless, and not something a civilised society should do. Punishment yes, but for the betterment of offender and society. A loose-loose is the last we want, no?