A Monte Carlo study of the compatibilization of A/B polymer blends has been performed using the bond fluctuation model. The considered compatibilizers are copolymer molecules composed of A and B blocks. Different types of copolymer structures have been included, namely, linear diblock and 4-block alternating copolymers, star block copolymers, miktoarm stars, and zipper stars. Zipper stars are composed of two arms of diblock copolymers arranged in alternate order (AB and BA) from the central unit, along with two homogeneous arms of A and B units. The compatibilization performance has been characterized by analyzing the equilibration of repulsion energy, the simulated scattering intensity obtained with opposite refractive indices for A and B, the profiles along a coordinate axis, the radial distribution functions, and the compatibilizer aggregation numbers. According to the results, linear alternate block copolymers, star block copolymers, and zipper stars exhibit significantly better compatibilization, with zipper stars showing slightly but consistently better performance.