•Numerical investigation of an industrial gas turbine lean premixed burner through a high-fidelity CFD approach.•Validation of the numerical setup through a direct comparison with experimental data.•Assessment of the flame shape prediction of two enhanced versions of the FGM and ATF combustion models.•Remarkable accuracy in predicting the flame topology exhibited by both models.•Assessment of both turbulent combustion models in supporting burner design phase. In the pursuit of decarbonization, the reduction of greenhouse gas emissions from power generation through gas turbine (GT) engines plays a crucial role in the whole industrial sector. As industries strive to transition towards cleaner energy sources, the design and optimization of novel GT burners require a deep comprehension of the complex interaction between fluid dynamics and combustion processes embedded within the system. Computational Fluid Dynamics (CFD) plays a pivotal role in these processes by providing valuable insights into the complex flow patterns, flame topology, and stability limits within the combustor. Concurrently, the burner design phase necessitates a considerable number of simulations to ascertain flame stability limits under various burner designs and operating conditions. Therefore, it is imperative to control computational costs while ensuring a high level of accuracy. The present work is focused on a comprehensive comparative analysis of two widely employed turbulent combustion closure models: the Flamelet Generated Manifold (FGM) and the Artificially Thickened Flame (ATF). Both models utilize extended versions with specific modifications aimed at effectively addressing their respective limitations. The investigation is performed through a Large Eddy Simulation (LES) based CFD analysis within the context of a lean premixed burner designed by Baker Hughes and operated with methane at atmospheric pressure. The primary benchmark for numerical validation will be provided by detailed chemiluminescence images from a test campaign conducted by the University of Florence, thereby yielding valuable insights into flame topology and positioning. Furthermore, potential disparities in the flow field and fuel concentration at the burner exit between the two models will be revealed.