We compare and contrast the microstructure, viscoelastic properties, and shock response of coarse-grained models of multiblock copolymer and diblock copolymers using molecular dynamics simulations. This study is motivated by the excellent dissipative and shock-mitigating properties of polyurea, speculated to arise from its multiblock chain architecture. Our microstructural analyses reveal that the multiblock copolymer microphase-separates into small, interconnected, rod-shaped, hard domains surrounded by a soft matrix, whereas the diblock copolymer forms larger, unconnected, hard domains. Our viscoelastic analyses indicate that compared with the diblock copolymer, the multiblock copolymer is not only more elastic but also more dissipative, as signified by its larger storage and loss modulus at low to intermediate frequencies. Our shock simulations and slip analyses reveal that shock waves propagate slower in the multiblock copolymer in comparison with the diblock copolymer, most likely due to the more deformable hard domains in the former system. These results suggest that the multiblock architecture of polyurea might impart polyurea with smaller, more deformable, and interconnected hard domains that lead to improved energy dissipation and lower shock speeds.