We extend the study of efficient profiled attacks on masking schemes initiated by Lerman and Markowitch (TIFS, 2019) in different directions. First, we study both the profiling complexity and the online attack complexity of different profiled distinguishers. Second, we extend the range of the noise levels of their experiments, in order to cover (higher-noise) contexts where masking is effective. Third, we further contextualize the investigated distinguishers (e.g., in terms of adversarial capabilities and a priori assumptions on the leakage probability density function). Finally, we complete the list of distinguishers considered in this previous work and add expectation-maximization, soft analytical side-channel attacks and multi-layer perceptrons in our comparisons. Our results allow shedding an interesting new light on the respective strengths and weaknesses of these different statistical tools, both in the context of a side-channel security evaluation and for concrete attacks. In particular, they confirm the experimental relevance of evaluation shortcuts leveraging the masking randomness during profiling, in order to speed up the evaluation process.