Conducting polymers based hexagonal boron nitride (h-BN) nanocomposites i.e. polyaniline (PANI)/h-BN and polyaniline -polypyrrole (PANI-PPy)/h-BN were fabricated through chemical oxidative polymerization approach. The structural, thermal, morphological, and electrochemical properties of the prepared materials were studied extensively. FTIR and XRD patterns revealed the successful fabrication of desired nanocomposites. TGA analysis showed that the presence of h-BN increases the thermal stability of both the nanocomposites (PANI/h-BN and PANI-PPy/h-BN). All the prepared materials demonstrated irregular and aggregated morphological structures with the diameters remained almost similar (100 nm). The electrochemical performance of the materials was evaluated by cyclic voltammetry (CV), electrochemical impedance (EIS) and galvanostatic charge-discharge (GCD) in three electrodes and two electrodes systems. The prepared PANI/h-BN nanocomposites exhibited the highest capacitance (927 F/g) and capacitance retention (97.6%) after 100 cycles compared to the others. The Tafel extrapolation study shows less corrosion rate for PANI/h-BN electrode, and EIS indicate higher energy storage capacity of the PANI/h-BN electrode compared to PANI-PPy/h-BN electrode. Finally, a set of hybrid asymmetric supercapacitor was successfully constructed using the synthesized nanocomposites as positive electrode and activated carbon (AC) as negative electrode. The assembled device PANI/h-BN//AC showed the highest sp. capacitance (343 F/g), power density (921 W/kg), and it lit up a 5 mm green LED for 200 min, indicating its superiority over the other supercapacitor device.