The dynamic mechanical behavior and energy absorption characteristics of nano-enhanced functionally graded composites, consisting of 3 layers of vertically aligned carbon nanotube (VACNT) forests grown on woven fiber-glass (FG) layer and embedded within 10 layers of woven FG, with polyester (PE) and polyurethane (PU) resin systems (FG/PE/VACNT and FG/PU/VACNT) are investigated and compared with the baseline materials, FG/PE and FG/PU (i.e., without VACNT). A Dynamic Mechanical Analyzer (DMA) was used for obtaining the mechanical properties. It was found that FG/PE/VACNT exhibited a significantly lower flexural stiffness at ambient temperature along with higher damping loss factor over the investigated temperature range compared to the baseline material FG/PE. For FG/PU/VACNT, a significant increase in flexural stiffness at ambient temperature along with a lower damping loss factor was observed with respect to the baseline material FG/PU. A Split Hopkinson Pressure Bar (SHPB) was used to evaluate the energy absorption and strength of specimens under high strain-rate compression loading. It was found that the specific energy absorption increased with VACNT layers embedded in both FG/PE and FG/PU. The compressive strength also increased with the addition of VACNT forest layers in FG/PU; however, it did not show an improvement for FG/PE.