My cake and eat it too.

Someone please explain why when a foreign national is subject to possible prosecution in the US for a crime that carries the death penalty, they demand to be returned to "their home country" for trial? But when it is not capital punishment involved, they want to be tried in the US instead? Is it so simple as capital punishment in US=no good, torture in homeland = no good.
I have an idea, just STOP commiting crimes in my country, OK? But please, keep these stupid, pointless, when is it OK to be a terrorist, crap off the screen.