Both failures of the Prison Service in their own way.
The point is, these are known criminals who are no longer at liberty to attack unsuspecting members of the public, which is precisely what the "but it will stop them killing other people" argument revolves around.
Yes, in some cases they will clearly remain a threat to prison staff and other inmates, but the key difference is they are in a confined facility, not at large in the community, they are known to those with the duty of care, not moving around unknown to the general public, and therefore there is knowledge of who and what they are and preventative steps can be taken to pre-empt future problematic behaviour.
A lack of proper procedure, care and attention, or facilities post-incarceration is not a justification for bringing back execution, it's an institutional failure, the causes of which need determined and put right.
There is also another point to bear in mind -
The study of criminality is vital in itself in order to prevent and detect future potential crime. The reason we don't really see prolific serial-killers any more is because of past study of known serial-killers leading to the development of techniques like criminal profiling. If you simply execute anyone aberrant, you totally preclude the ability to study them and learn from them, and then use that learned knowledge to understand and predict aberrant behaviour, therefore saving lives because of the fact people doing similar things in the future are detected and apprehended more quickly.
Aberrant people, including the ones people find more repellent like serial-killers, murderous paedophiles, torturers and so on, all exist as part of society whether people like that or not, so killing them out of hand does not, in any way, help society to understand why they exist, what motivates and drives them, how they operate, how they stay hidden, how they select victims etc etc. You can not solve a sociological problem by only removing all known examples of the problem and then calling it job done, because there will invariably be the ones missed because you are operating on an reactive and not proactive basis, you don't understand what it is you are dealing with, and then there will always be new ones popping up to replace the old simply because they occur naturally in the population in any case.
Like it or not, murderers, paedophiles, sexual sadists and the like are a learning opportunity, and it's stupidly closed-minded to think they are not, because refusing to learn from them just enables future versions of precisely the same thing.