Fluid viscous devices are often employed to control and enhance the seismic performance of structural systems. The reliability, under seismic events, of systems equipped with such type of devices is strongly affected by the reliability of the devices themselves. Indeed, in case of early disruption of one or more dampers, the structure might be unable to withstand the seismic action, due to the potential lack of inner dissipative capacity. With focus on buildings equipped with linear and nonlinear viscous dampers, the seismic reliability level ensured by the current design criteria proposed by the main international seismic codes is critically assessed by using a probabilistic approach. A steel building benchmark case study is considered, and both linear and nonlinear dampers are designed in order to produce the same target structural performance under a given seismic hazard level; afterwards, the performance variations due to changes in the damper nonlinearity level is assessed by comparing the demand hazard curves of the most significant global and local response parameters. Finally, a sensitivity analysis of the seismic risk with respect to uncertain damper properties is carried out, by using the reliability-based optimization approach recently proposed by the authors. A comparison with code provisions shows that amplification factors currently used for the structural design provide non-homogeneous safety levels and should be improved by better considering the response variations due to damper degree of nonlinearity as well as the variability of the viscous damper properties due to manufacturing process. Results provide useful insights for a future improvement of the seismic code’ prescriptions concerning the design of fluid viscous dampers.