Wind and/or earthquake-imposed loadings on two dynamically similar adjacent buildings cause vigorous shaking that can be mitigated using energy dissipating devices. Here, the vibration response control in such adjacent structures interconnected with semi-active magneto-rheological (MR) dampers is studied, which could also be used as a retrofitting measure in existing structures apart from employing them in new constructions. The semi-active nature of the MR damper is modeled using the popular Lyapunov control algorithm owing to its least computational efforts among the other considered control algorithms. The semi-active performance of the MR damper is compared with its two passive states, e.g., passive-off and passive-on, in which voltage applied to the damper is kept constant throughout the occurrence of a hazard, to establish its effectiveness even during the probable electric power failure during the wind or seismic hazards. The performance of the MR damper, in terms of structural response reduction, is compared with other popular energy dissipating devices, such as viscous and friction dampers. Four damper arrangements have been considered to arrive at the most effective configuration for interconnecting the two adjoining structures. Structural responses are recorded in terms of storey displacement, storey acceleration, and storey shear forces. Coupling the two adjacent dynamically similar buildings results in over a 50% reduction in the structural vibration against both wind and earthquake hazards, and this is achieved by not necessarily connecting all the floors of the structures with dampers. The comparative analysis indicates that the semi-active MR damper is more effective for response control than the other passive dampers.