In the context of non-destructive testing and evaluation research community, global sensitivity analysis (GSA) methods are widespread tool for quantifying the sensitivity of measurements with respect to the variation of inputs over the whole design space. For parameter ranking purposes, GSA methods have been historically preferred by NDT&E scholars comparared to machine learning (ML) approaches based on feature importance (FI) techniques such as random forest-based, SHAP values, etc. For practical application, the use of GSA and FI can face limitations when the number of evaluations of the physical model is very high. That is, the main issues that one needs to face with GSA and FI on practical problems is the low CPU time efficiency of the numerical solver and/or the high cardinality (i.e., the number of inputs) of the problem considered. This paper targets two main goals. First, we proposes to tackle the problem of an efficient GSA and FI procedure relying to a tailored deep neural network to be employed as metamodel (or surrogate model) as replacement of the less efficient numerical model. Second, we compare GSA (i.e., Sobol' indices and \delta-sensitivity measure) indices and FI (i.e., SHAP) method for parameters ranking purposes. In particular, we describe a generative deep neural network framework to be straightforwardly applied to GSA and FI studies. The numerical experiments considered in this communication correspond to an eddy current testing inspection problem where multiple arbitrarily oriented cracks are lying in a conductive planar multilayered structure.