Honestly, as a native speaker, I would prefer using "Option" in this context because "Option" puts more emphasis on the fact that you have a choice. "Der Tod ist die letzte Moeglichkeit" sounds less natural to me. "Der letzte Ausweg" would be good, too. Hope that helped a bit ;-)

to me (native as well) both is the same. Option sounds a little better, but i don't see a difference in the meaning. of course like Meike said you can say "der letzte Ausweg too".