Who are these directors and can you list their movies?
Let me start with two disclaimers. One, we are all playing a subjective game here, and, two, I have no problem with anybody's list.
That being said, you have posed a very simplistic question about how one should judge "greatness.". Art isn't a basketball game where one adds up two directors' best movies and if one guy has more "great" movies than the other guy, that guy wins. I mean, I like Spielberg, though I would not call most of his movies "great" by even the most casual use of that adjective. From your list, I would prune:
The Color Purple; Hook; Amistad, Minority Report, Catch Me If You Can; Ready Player One; and after the first brilliant twenty minutes,
Saving Private Ryan. Spielberg can be a wonderfully entertaining director for which, in my case,
Jaws, ET, and the first
Raiders attest. But the only movies of his that have ever made me think, even a little, are
Schindler's List,
Munich and to a lesser extent
Empire of the Sun. He has made popcorn into a near art form, but it is still popcorn. In my book, his best works are a lot of fun, but overly sentimentalized and shallow, too. Greatest popcorn director? I'm not sure I would give him that title, even. Greater than Alfred Hitchcock, Charlie Chaplin, John Ford, Akira Kurosawa, the latter three who often made me think, as well?
I'm not trying to dump on your favourite guy, just to suggest why some people might not share the amount of enthusiasm toward him that you do. My major point is that one shouldn't try to judge art, whatever your standards are, by the pound. Just about all the directors listed on this thread have several movies that one could argue are "great." But it's not like it's a box score: Fellini 5, Welles 3. Art isn't a commodity. Any given work needs to be judged on its own merits, and quantification adds no insight. Some of these directors like Bergman, Kurosawa and Godard made a ton of movies while other directors such as Tarkovsky, Leone and Erice made a dozen movies or fewer. It is more a question of the quality of works that they create, not the quantity. Erice's works are no less superb than anybody else's because he only made four of them. To put it simplistically myself, some directors may have a higher floor but other directors can have a higher ceiling, and for me, that's where most of the great movies can be found.