The optical properties of the wurtzite (WZ) GaAs crystal phase found in nanowires (NWs) are a highly controversial topic. Here, we study high-quality pure WZ GaAs/AlGaAs core-shell NWs grown by Au-assisted molecular beam epitaxy (MBE) with microphotoluminescence spectroscopy (μ-PL) and (scanning) transmission electron microscopy on the very same single wire. We determine the room temperature (294 K) WZ GaAs bandgap to be 1.444 eV, which is ∼20 meV larger than in zinc blende (ZB) GaAs, and show that the free exciton emission at 15 K is at 1.516 eV. On the basis of time- and temperature-resolved μ-PL results, we propose a Γ(8) conduction band symmetry in WZ GaAs. We suggest a method for quantifying the optical quality of NWs, taking into consideration the difference between the room and low temperature integrated PL intensity, and demonstrate that Au-assisted GaAs/AlGaAs core-shell NWs can have high PL brightness up to room temperature.