The three dimensional carrier confinement in GaN nanodiscs embedded in GaN/AlGaN nanowires and its effect on their photoluminescence properties is analyzed for Al concentrations between x = 0.08 and 1. Structural analysis by high resolution transmission electron microscopy reveals the presence of a lateral AlGaN shell due to a composition dependent lateral growth rate of the barrier material. The structural properties are used as input parameters for three dimensional numerical simulations of the confinement which show that the presence of the AlGaN shell has to be considered to explain the observed dependence of the emission energy on the Al concentration in the barrier. The simulations reveal that the maximum in the emission energy for x ~ 30% is assigned to the smallest lateral strain gradient and consequently the lowest radial internal electric fields in the nanodiscs. Higher Al-concentrations in the barrier cause high radial electric fields that can overcome the exciton binding energy and result in substantially reduced emission intensities. Effects of polarization-induced axial internal electric fields on the photoluminescence characteristics have been investigated using nanowire samples with nanodisc heights ranging between 1.2 nm and 3.5 nm at different Al concentrations. The influence of the quantum confined Stark effect is significantly reduced compared to GaN/AlGaN quantum well structures which is attributed to the formation of misfit dislocations at the heterointerfaces which weakens the internal electric polarization fields.