The seismic performance of structures can substantially be improved by incorporating supplemental dampers. Of these, fluid viscous dampers (FVDs) and friction dampers (FDs) have gained such commercial standing that they can be accessed off the shelf as per the requirements. For a building, it would be of interest to know how the choice of a particular damper system should be made. Given this, the present study is focused on the comparison of the design and performance of these two devices. A steel building with vertical setbacks is selected for this purpose. The supplemental damping required to be provided by the dampers is determined using the Capacity Spectrum Method. The damper design includes the determination of the design characteristics of FVDs and FDs, such as the damping coefficients of FVDs and the slip loads of FDs. These design parameters are obtained based on the approach of story shear strain energy proportional distribution. Since brace stiffness affects the performance of dampers, an iterative study is conducted to obtain the optimal stiffness of the brace incorporating the dampers. Further, considering its advantage over the linear counterpart, nonlinear FVD is considered in the present study. The effectiveness of the dampers is assessed through nonlinear dynamic analyses of the uncontrolled and controlled building structure under recorded seismic excitations. Results indicate that both the acceleration and displacement responses of the building with vertical irregularity can be well-controlled with the provision of the proposed damper schemes. However, FDs achieve a larger reduction in the displacement response for strong ground motion, while FVDs are more effective in acceleration response control.