In performance‐based earthquake engineering, the suitability of an intensity measure (IM) is expressed through its efficiency and sufficiency. An efficient IM leads to a small record‐to‐record variability in the estimation of demand given seismic intensity. A sufficient IM is one that renders the estimation of demand for all intensity levels independent of all other ground motion parameters. Given that establishing sufficiency is not a trivial task, the relative sufficiency measure (RSM) has been proposed previously based on information theory concepts. RSM can be employed for quantifying the relative sufficiency of an IM with respect to another IM by the amount of extra information that it relays on average about the ground motion for the estimation of a demand parameter of interest. RSM has been so far conditioned on a linear logarithmic regression probability model, better known as the Cloud Analysis (CA), which relies on unscaled ground‐motion records. This work lays out the methodology for estimating both the efficiency and RSM in terms of the damage measure directly (instead of demand parameter) and by employing alternative nonlinear dynamic analysis procedures (NDAPs), such as, a modified version of CA that considers the collapse‐cases explicitly and the incremental dynamic analysis. It is demonstrated that the RSM can be sensitive to the NDAP employed, while it does not demonstrate significant sensitivity to the limit state of interest. An alternative measure of efficiency (known in literature as proficiency), directly measured as the dispersion in the fragility curve, shows more sensitivity to the limit state.