And he was a far more important writer

With all due respects, mav, my good friend and colleague, but in degree of importance and stature O'Neill towers over Miller. Without Eugene O'Neill there would be NO American theatre, he brought stature and respect to the American stage, was known as the "Father of the American Theatre", and to see his work well-produced is a revelation...plays like "The Iceman Cometh," "Long Day's Journey Into Night," "Moon for the Misbegotten," and "Anna Christie", among so many others, including his one-act sea-plays, will live forever as promethean achievements. Oh, and we was also the second US Nobel Laureate and only US playwright to be awarded such.

In a line of importance I would have to say it is O'Neill, Tennessee Williams, and then Arthur Miller...all titans of the stage.