Semiconductor nanowires (NWs) offer unique opportunities for next-generation optoelectronic devices. In this work, we investigate charge carrier diffusion induced branched NW light-emitting diodes (LEDs) with designed bandgap heterojunctions. Emission from epitaxially grown arrays of direct bandgap branch NWs on indirect bandgap GaInP core NWs is characterized. We significantly suppress radiative recombination in the indirect bandgap core while promoting carrier diffusion toward the branches. Temperature-dependent electroluminescence measurements reveal different recombination mechanisms in the indirect bandgap core and direct bandgap branch NWs. Dominant branch emission is achieved by use of indirect bandgap core NWs, which enables the design of monochromatic branched NW LEDs with potentially high light extraction efficiency. These results demonstrate an attractive pathway toward high efficiency NW-based LEDs.