Actually, Arnold was already quite well known, and had several film credits to his name. If anything laucnhed him into the "stratosphere", it was T2 (or Kindergarten Cop, I've never been able to pinpoint it.)
Die Hard, however, DID launch Bruce Willis into the A-List stratosphere. John McClane is a classic American hero, and not even close to the stereotypical hero. He doesn't do what he does because he wants to. He does it because there's no one else that can do what needs to be done. And I think people are forgetting how great the plot to Die Hard actually is. Most action films up to that point were either
A) Terrorists take over _____, hero kills them, or
B) Hero stops villains from accomplishing a heist of ____
Classic villain Hans Gruber's plan is ingenious; Pose as terrorists to distract the cops and FBI from their actual target; hundreds of millions of dollars in bonds. The film is very original, and re-wrote the book on action films, which had, at the time, been dominated by Rambo and Death Wish wannabes, with no substance and a flimsy plot. And THAT's why Die Hard is considered to be the greatest action film of all time, and is definitely better than Terminator.