Process-based models can be usefully employed for the assessment of field and regional-scale impact of drought on crop yields. However, in many instances, especially when they are used at the regional scale, it is necessary to identify the parameters and input variables that most influence the outputs and to assess how their influence varies when climatic and environmental conditions change. In this work, two different crop models, able to represent yield response to water, Aquacrop and SAFYE, were compared, with the aim to quantify their complexity and plasticity through Global Sensitivity Analysis (GSA), using Morris and EFAST (Extended Fourier Amplitude Sensitivity Test) techniques, for moderate to strong water limited climate scenarios. Although the rankings of the sensitivity indices was influenced by the scenarios used, the correlation among the rankings, higher for SAFYE than for Aquacrop, assessed by the top-down correlation coefficient (TDCC), revealed clear patterns. Parameters and input variables related to phenology and to water stress physiological processes were found to be the most influential for Aquacrop. For SAFYE, it was found that the water stress could be inferred indirectly from the processes regulating leaf growth, described in the original SAFY model. SAFYE has a lower complexity and plasticity than Aquacrop, making it more suitable to less data demanding regional scale applications, in case the only objective is the assessment of crop yield and no detailed information is sought on the mechanisms of the stress factors affecting its limitations.