GaAs/AlGaAs core-shell nanowires (NWs) were grown on Si(111) by Ga-assisted molecular beam epitaxy via the vapor-liquid-solid mechanism. High-resolution and scanning transmission electron microscopy observations showed that NWs were predominantly zinc-blende single crystals of hexagonal shape, grown along the [111] direction. GaAs core NWs emerged from the Si surface and subsequently, the NW growth front advanced by a continuous sequence of (111) rotational twins, while the AlGaAs shell lattice was perfectly aligned with the core lattice. Occasionally, single or multiple stacking faults induced wurtzite structure NW pockets. The AlGaAs shell occupied at least half of the NW's projected diameter, while the average Al content of the shell, estimated by energy dispersive x-ray analysis, was x = 0.35. Furthermore, molecular dynamics simulations of hexagonal cross-section NW slices, under a new parametrization of the Tersoff interatomic potential for AlAs, showed increased atom relaxation at the hexagon vertices of the shell. This, in conjunction with the compressively strained Al0.35Ga0.65As shell close to the GaAs core, can trigger a kinetic surface mechanism that could drive Al adatoms to accumulate at the relaxed sites of the shell, namely along the diagonals of the shell's hexagon. Moreover, the absence of long-range stresses in the GaAs/Al0.35Ga0.65As core-shell system may account for a highly stable heterostructure. The latter was consolidated by temperature-dependent photoluminescence spectroscopy.