Except the Vex don't conflict with other subdivisions at all. The are a singular collective mind spread across many frames. The Vex search for what they dub an "emperor to all outcomes." This means they simulate every single possible scenario, and they act in some way to ensure that any of these possible chain of events end in Vex victory, or at least their continued survival. Because they are preparing for every scenario possible they must prepare just as many responses and project to fulfill each particular victory condition. The Vault of Glass and Black Garden are two such projects based upon information learned by Quria during his war with Oryx. They are not in a state competition but cooperation. They pursue different paths to the same goal so if either path ends up being the "correct" scenario the Vex as a whole win.