We report on the electron beam induced current (EBIC) microscopy and cathodoluminescence (CL) characterization correlated with compositional analysis of light emitting diodes based on core/shell InGaN/GaN nanowire arrays. The EBIC mapping of cleaved fully operational devices allows to probe the electrical properties of the active region with a nanoscale resolution. In particular, the electrical activity of the p-n junction on the m-planes and on the semi-polar planes of individual nanowires is assessed in top view and cross-sectional geometries. The EBIC maps combined with CL characterization demonstrate the impact of the compositional gradients along the wire axis on the electrical and optical signals: the reduction of the EBIC signal toward the nanowire top is accompanied by an increase of the CL intensity. This effect is interpreted as a consequence of the In and Al gradients in the quantum well and in the electron blocking layer, which influence the carrier extraction efficiency. The interface between the nanowire core and the radially grown layer is shown to produce in some cases a transitory EBIC signal. This observation is explained by the presence of charged traps at this interface, which can be saturated by electron irradiation.