The seismic design of optimal damped outrigger structures relies on the assumption that most of the input energy will be absorbed by the dampers, whilst the rest of the structure remains elastic. When subjected to strong earthquakes, nevertheless, the building structure may exhibit plastic hinges before the dampers begin to work. In order to determine to which extent the use of viscously damped outriggers would avoid damage, both the host structure's hysteretic behaviour and the dampers' performance need to be evaluated in parallel. This article provides a parametric study on the factors that influence the distribution of seismic energy in tall buildings equipped with damped outriggers: First, the influence of outrigger's location, damping coefficients, and rigidity ratios core‐to‐outrigger and core‐to‐column in the seismic performance of a 60‐story building with conventional and with damped outriggers is studied. In parallel, nonlinear behaviour of the outrigger with and without viscous dampers is examined under small, moderate, strong, and severe long‐period earthquakes to assess the hysteretic energy distribution through the core and outriggers. The results show that, as the ground motion becomes stronger, viscous dampers effectively reduce the potential of damage in the structure if compared to conventional outriggers. However, the use of dampers cannot entirely prevent damage under critical excitations.