There are so many angles to a question like this. From my limited experience/knowledge, I don't think it's just. I remember reading/watching something (I forgot where) that said capital punishment is just an act of revenge, not justice, which is true, isn't it?
To end one's life for a serious crime means they wouldn't have to suffer anymore - it's almost like they've won. They need to learn and accept the error of their ways and that is far more effective in a place like prison rather than having their life ended in a matter of minutes. Also, what if the the person put do death turns out to be innocent? How do you resolve that? It's irreversible.
My standpoint most probably differs from people who have, in fact, been victims of serious crimes but on the whole I don't think it is fair.