By employing various high-resolution metrology techniques we directly probe the material composition profile within GaAs-Al0.3Ga0.7As core-shell nanowires grown by molecular beam epitaxy on silicon. Micro Raman measurements performed along the entire (>10 μm) length of the [111]-oriented nanowires reveal excellent average compositional homogeneity of the nominally Al0.3Ga0.7As shell. In strong contrast, along the radial direction cross-sectional scanning transmission electron microscopy and associated chemical analysis reveal rich structure in the AlGaAs alloy composition due to interface segregation, nanofaceting, and local alloy fluctuations. Most strikingly, we observe a 6-fold Al-rich substructure along the corners of the hexagonal AlGaAs shell where the Al-content is up to x ~ 0.6, a factor of 2 larger than the body of the AlGaAs shell. This is associated with facet-dependent capillarity diffusion due to the nonplanarity of shell growth. A modulation of the Al-content is also found along the radial [110] growth directions of the AlGaAs shell. Besides the ~10(3)-fold enhancement of the photoluminescence yield due to inhibition of nonradiative surface recombination, the AlGaAs shell gives rise to a broadened band of sharp-line luminescence features extending ~150-30 meV below the band gap of Al0.3Ga0.7As. These features are attributed to deep level defects under influence of the observed local alloy fluctuations in the shell.