Fragility curves express the failure probability of a structure, or of a critical component, as a function of a seismic intensity measure, for a given failure criterion. The failure criterion is often based on the difference between a structural response parameter level and a threshold, which can be either deterministic or probabilistic. Within a probabilistic context, structural response parameters are random variables and therefore subjected to a certain variability mostly depending on the structural typology and the assessment method. When engineers have to make a decision to choose appropriate engineering demand parameters to be considered, they need to know how sensitive it will be. The study reported in this paper attempts to bring answers to this question. More precisely, the sensitivity of some engineering demand parameters is quantified and discussed as a function of the structural typology (beam-column or wall-based structures) and of the considered assessment method. The final output is a correlation matrix linking (i) the coefficient of variation of specific engineering demand parameters, (ii) the structural typology and (iii) the adopted modeling technique.