The ultimate purity of synthetic diamond crystals is currently limited by traces of boron and nitrogen. Here we study diamond crystals grown at high-pressure high-temperature, which are made of 3D growth sectors with variable residual impurity contents. The boron concentration is found in the 0.5-6.4 ppb range thanks to continuous cathodoluminescence (cw-CL) analysis. Time-resolved cathodoluminescence (TRCL) experiments complete the impurity analysis with measurements of free exciton lifetimes. From them, we deduced an estimate of the nitrogen concentration at the ppb level, from 0.6 to 30 ppb depending on the growth sectors. We identified n-type, p-type and highly compensated regions, which illustrates the potential of cathodoluminescence as a local probe for qualifying diamond for electronic and quantum applications.