We present a set of experimental results identifying various effects that govern the carrier dynamics of self-catalyzed GaAs/AlGaAs core-shell nanowires (NWs) grown by molecular beam epitaxy i.e. surface recombination velocity, surface charge traps, and structural defects. Time-resolved photoluminescence of NW ensemble and spatially-resolved cathodoluminescence of single NWs reveal that emission intensity, decay time and carrier diffusion length of the GaAs NW cores strongly depend on AlGaAs shell thickness but in a non-monotonic fashion. Although 7 nm-AlGaAs shell can efficiently suppress the surface recombination velocity of the GaAs NW cores, the effect of the band bending caused by the surface charges remains dominant if the shell thickness is less than 50 nm; that is, the carrier diffusion length is smaller in the NWs with a thinner shell caused by a stronger carrier scattering at the core/shell interface. If the AlGaAs shell thickness is larger than 50 nm, the luminescence efficiency of the GaAs NW cores starts to be deteriorated, ascribed to the defect formation inside the AlGaAs shell evidenced by transmission electron microscopy.