Analogous to planar heteroepitaxy, misfit dislocation formation and stress-driven surface roughening can relax coherency strains in misfitting core-shell nanowires. The effects of coaxial dimensions on strain relaxation in aligned arrays of Ge-core/Si-shell nanowires are analyzed quantitatively by transmission electron microscopy and synchrotron X-ray diffraction. Relating these results to reported continuum elasticity models for coaxial nanowire heterostructures provides valuable insights into the observed interplay of roughening and dislocation-mediated strain relaxation.