Industrial and environmental granular flows commonly exhibit a phenomenon known as ``granular segregation," in which grains separate according to physical characteristics (size, shape, density), interfering with industrial applications (cement mixing, medicine and food production) and fundamentally altering the behavior of geophysical flows (landslides, debris flows, pyroclastic flows, riverbeds). While size-induced segregation has been well studied, the role of grain shape is not well understood. Here we conduct numerical experiments to investigate how grain shape affects granular segregation due to grain-grain and grain-fluid interactions. To isolate the former, we compare dry, bidisperse mixtures of spheres alone with mixtures of spheres and cubes in a rotating drum. Results show that while segregation generally increases with particle size ratio, the presence of cubes decreases segregation levels compared to cases with only spheres. Further, we find hysteresis in segregation trends with size ratio; segregation is lowest when the small grains are cubic as they approach a jammed state with reduced mobility. We find similar hysteresis in simulations of a shear-driven coupled fluid-granular flow (e.g., a riverbed), demonstrating that this phenomenon is not unique to rotating drums; however, in contrast to the dry system, we find that total segregation increases in the presence of cubic grains, and fluid drag effects can qualitatively change segregation trends. Our findings demonstrate competing shape-induced segregation patterns in wet and dry flows—independently from grain size controls—with implications for many industrial and geophysical processes.