In this paper, we show the carbonization of binary composites consisting of graphene nanoplatelets and melamine (GNP/MM), multi-walled carbon nanotubes and melamine (CNT/MM) and trinary composites containing GNP, CNT, and MM. Additionally, the manuscript presents results on the influence of structural factors for the electrochemical performance of carbon composites on their catalytic activity. This study contributes to the wide search and design of novel hybrid carbon composites for electrochemical applications. We demonstrate that intensive nitrogen atom insertion is not the governing factor since hybrid system modifications and porous structure sometimes play a more crucial role in the tailoring of electrochemical properties of the carbon hybrids seen as a noble metal-free alternative to traditional electrode materials. Additionally, HRTEM and Raman spectra study allowed for the evaluation of the quality of the obtained hybrid materials.