Considerable efforts are currently being made by several international working groups focused on the development of generic, also known as simplified or standard, wind turbine models for power system stability studies. In this sense, the first edition of International Electrotechnical Commission (IEC) 61400-27-1, which defines generic dynamic simulation models for wind turbines, was published in February 2015. Nevertheless, the correlations of the IEC generic models with respect to specific wind turbine manufacturer models are required by the wind power industry to validate the accuracy and corresponding usability of these standard models. The present work conducts the validation of the two topologies of variable speed wind turbines that present not only the largest market share, but also the most technological advances. Specifically, the doubly-fed induction machine and the full-scale converter (FSC) topology are modeled based on the IEC 61400-27-1 guidelines. The models are simulated for a wide range of voltage dips with different characteristics and wind turbine operating conditions. The simulated response of the IEC generic model is compared to the corresponding simplified model of a wind turbine manufacturer, showing a good correlation in most cases. Validation error sources are analyzed in detail, as well. In addition, this paper reviews in detail the previous work done in this field. Results suggest that wind turbine manufacturers are able to adjust the IEC generic models to represent the behavior of their specific wind turbines for power system stability analysis.