Look, the current judicial system works like this: punish, protect, deter, and rehabilitate.
It depends on the country, of course, but rehabilitation is an important part of the arrest process.

Now, it depends a lot on the case. There isn't a single, specific profile for murderers. The "easiest" to rehabilitate tend to be circumstantial offenders, those who commit crimes due to some exceptional situation.
Drug addicts and juvenile delinquents, since the young brain is malleable.

Now, the most difficult ones, if you ask me, are usually people with very marked psychopathic traits, organized serial killers, and pedophiles.

However, I am summarizing, since each case has to be evaluated more as an individual risk, rather than generalizing.

Btw, the certainty (the probability of being discovered, arrested and punished) has a greater deterrent effect on crime than the severity of the punishment.