This study compares the damping behavior of boron nitride nanotubes (BNNTs) and carbon nanotubes (CNTs) as reinforcement in PLC, a biodegradable copolymer. The damping behavior of PLC composites reinforced with 2 wt % or 5 wt % nanotube filler is evaluated by nanodynamic mechanical analysis (NanoDMA). The addition of 2 wt % CNT leads to the greatest enhancement in damping (tan δ) behavior. This is attributed to pullout in CNTs because of lower interfacial shear strength with the polymer matrix and a more effective sword-in-sheath mechanism as opposed to BNNTs which have bamboo-like nodes. BNNTs however have a superior distribution in the PLC polymer matrix enabling higher contents of BNNT to further enhance the damping behavior. This is in contrast with CNTs which agglomerate at higher concentrations, thus preventing further improvement at higher concentrations. It is observed that for different compositions, tan δ values show no significant changes over varying dynamic loads or prolonged cycles. This shows the ability of nanotube mechanisms to function at varying strain rates and to survive long cycles.