Is anyone's ego inflated enough to end the debate on which "type" of art is more "important" than others? Well, I'll take their side and argue why Constructivism could be more important than other art movements. My main point would be "important" in the art world could be construed as "influential", whereas, in Constructivism, important meant more about being useful, and, to relate to the previous definition, influential not on other art movements, but, more importantly, on the masses. Instruction manuals are Constructivist; as a movement, it was born post-WWI as an embracement of propaganda posters as the modern way of reaching - more precisely, influencing - the populace.
If Constructivism can be analogous to the military and other art forms to fashion - ephemeral, fleeting, ultimately faded away - then, military wins. As long as humans will need an organized system of defense for themselves against other humans, and a need to reach and manipulate people to that end, then Constructivism could be considered superior to other art forms simply by virtue of its inextricability with those elements of human nature which will not, like fashion, fade any time soon.
