In the experimental electroluminescence (EL) spectra of light-emitting diodes (LEDs) based on N-polar (In,Ga)N/GaN nanowires (NWs), we observed a double peak structure. The relative intensity of the two peaks evolves in a peculiar way with injected current. Spatially and spectrally resolved EL maps confirmed the presence of two main transitions in the spectra, and suggested that they are emitted by the majority of single nano-LEDs. In order to elucidate the physical origin of this effect, we performed theoretical calculations of the strain, electric field, and charge density distributions both for planar LEDs and NW-LEDs. On this basis, we simulated also the EL spectra of these devices, which exhibit a double peak structure for N-polar heterostructures, both in the NW and the planar case. In contrast, this feature is not observed when Ga-polar planar LEDs are simulated. We found that the physical origin of the double peak structure is a stronger quantum-confined Stark effect occurring in the first and last quantum well of the N-polar heterostructures. The peculiar evolution of the relative peak intensities with injected current, seen only in the case of the NW-LED, is attributed to the three-dimensional strain variation resulting from elastic relaxation at the free sidewalls of the NWs. Therefore, this study provides important insights on the working principle of N-polar LEDs based on both planar and NW heterostructures.