There are actually several points that make it different:
The europeanEuropean charter of fundamental rights states in its very first article, that human dignity is invioableinviolable. (Just like the German Basic Law btw.) This automatically forbids any action of the state taking the life of any human being as a form of sanction.
Also people on death row usually wait for several years before the sentence is carried out and that is deemed as violating the human dignity as well. If you sit there years waiting for your execution that is deemed as damaging as torture.
The criminal system can and does fail. There are several well documented cases of people being treated unjustunjustly by the system and even falsely convicted for crimes they did not commit. You can release someone whom you imprisoned for life. You can't release someone you executed, you can just bury him.
Because even lifetime imprisonment is not what it says. The EuGHECJ (European Court of Justice) ruled that it is unconstitutional to imprison a person for life without the chance of parole. You might be imprisoned for a very long time, but there always has to be the chance forof parole.
The idea behind the justice system in Europe is not only to punish an offender. It is twofold,: first it should protect the public from a dangerous individual and, second, it should try to educate that individual to return to a lawful life - and well you can't re-educate a dead person. You can however grant him parole if he improves while imprisoned.