I notice we keep dipping back into the 19th century for some of these. For strictly 20th century, I'd say, in no particular order,
Helmut (Newton - note inclusion does not mean endorsement)
Ansel (Adams)/Edward (Weston)/Aaron (Siskind) Three-way tie.
I'm leaving Stieglitz and Steichen and the Pictorialists off of the 20th century list because Pictorialism was already dying by the 1920s, and the dominant 20th century aesthetic has been Modernist/post-Modernist.