Lincoln Michel is on the right track in using literary categories to differentiate between Boyhood and Birdman. He argues the latter belongs to the magical category, while the former is realist.
The “magician” school changes in part because that school’s credo is “make it new”; the aim is to push boundaries and flex one’s artistic muscles with ambitious conceits and ferocious style. For the realist school, the ethos is staying “true to life,” and the goal is to move the reader with honesty and truth. Flashy voice, style, or structure merely “gets in the way” of the “simple, honest story.”
The analogy between the literary and filmic categories isn’t precise because of the different histories of each medium. Iñárritu’s long takes have long been associated with cinematic realism, while Linklater’s seamless edits between periods of time violates classical Hollywood style by not situating us in time and place.
On the surface, Birdman seems to be the more stylistically daring film. Iñárritu’s techniques are wider-ranging than Linklater’s. However, I think Boyhood is actually more of a stylistic outlier in the context of contemporary American filmmaking if only because of Linklater’s stubborn adherence to cinematic realism. The only filmmakers working right now who use realist techniques with the same daring are the Dardenne brothers and Cristian Mungiu.