The Rogochover says that murder is so heinous that we even execute an insane person (ubiarta et hara mikirbecha). Rav Zilberstein disagrees. Rav Moshe, in a letter to then NY Gov. Hugh Carey (IM CM 2:68) says that someone who kills because of a cruel nature should be executed because of tikkun hamedina.
Of course, every measure must be taken to be sure that the right person is executed. However, giving him life imprisonment means that the public will have to pay for his upkeep his whole life, he can commit crimes in prison, escape, etc.
So far as a psychopath is concerned, Rambam says (Guide 1:7) that he is not really human but a sheid. Thus it would seem that he should be put down as is a mad dog.