Nanostructures have many material, electronic, and optical properties that are not found in bulk systems and that are relevant for technological applications. For example, nanowires realized from III-V semiconductors can be grown into a wurtzite crystal structure. This crystal structure does not naturally exist in bulk where these materials form the zinc-blende counterpart. Being able to concomitantly grow these nanowires in the zinc-blende and/or wurtzite crystal structure provides an important degree of control for the design and optimization of optoelectronic applications based on these semiconductor nanostructures. However, the refractive indices of this new crystallographic phase have so far not been elucidated. This shortcoming makes it impossible to predict and utilize the full potential of these new nanostructured materials for optoelectronics applications: a careful design and optimization of optical resonances by tuning the nanostructure geometry is needed to achieve optimal performance. Here, we report and analyze striking differences in the optical response of nanophotonic resonances in wurtzite and zinc-blende InAs nanowire arrays. Specifically, through reflectance measurements we find that the resonance can be tuned down to λ ≈ 380 nm in wurtzite nanowires by decreasing the nanowire diameter. In stark contrast, a similar tuning to below λ ≈ 500 nm is not possible in the zinc-blende nanowires. Furthermore, we find that the wurtzite nanowires can absorb twice as strongly as the zinc-blende nanowires. We attribute these strikingly large differences in resonant behavior to large differences between the refractive indices of the two crystallographic phases realized in these nanostructures. We anticipate our findings to be relevant for other III-V materials as well as for all material systems that manifest polytypism. Taken together, our results demonstrate crystal phase engineering as a potentially new design dimension for optoelectronics applications.