Whether two species will co-crystallize depends on the chemical, physical and structural complementarity of the interacting components. Here, by using DNA as a surface ligand, we selectively co-crystallize mixtures of two different anisotropic nanoparticles and systematically investigate the effects of nanoparticle size and shape complementarity on the resultant crystal symmetry, microstrain, and effective 'DNA bond' length and strength. We then use these results to understand a more complicated system where both size and shape complementarity change, and where one nanoparticle can participate in multiple types of directional interactions. Our findings offer improved control of non-spherical nanoparticles as building blocks for the assembly of sophisticated macroscopic materials, and provide a framework to understand complementarity and directional interactions in DNA-mediated nanoparticle crystallization.