Turbulent combustion models for Large Eddy Simulation (LES) aims at predicting the flame dynamics. So far, they have been proven to predict correctly the mean flow and flame properties in a wide range of configurations. A way to challenge these models in unsteady situations is to test their ability to recover turbulent flames submitted to harmonic flow modulations. In this study, the Flame Transfer Function (FTF) of a CH4/H2/air premixed swirled-stabilized flame submitted to harmonic flowrate modulations in a non-adiabatic combustor is compared to the response computed using the Filtered TAbulated Chemistry for LES (F-TACLES) formalism. Phase averaged analysis of the perturbed flow field and flame response reveal that the velocity field determined with Particle Image Velocimetry measurements, the heat release distribution inferred from OH* images and the probability of presence of burnt gases deduced from OH-Planar Laser Induced Fluorescence measurements are qualitatively well reproduced by the simulations. However, noticeable differences between experiments and simulations are also observed in a narrow frequency range. A detailed close-up view of the flow field highlight differences in experimental OH* and numerical volumetric heat release rate distributions which are at the origin of the differences observed between the numerical and experimental FTF. These differences mainly originate from the outer shear layer of the swirling jet where a residual reaction layer takes place in the simulations which is absent in the experiments. Consequences for turbulent combustion modeling are suggested by examining the evolution of the perturbed flame brush envelope along the downstream distance of the perturbed flames. It is shown that changing the grid resolution and the flame subgrid scale wrinkling factor in these regions does not alter the numerical results. It is finally concluded that the combined effects of strain rate and enthalpy defect due to heat losses are the main factors leading to small but sizable differences of the flame response to coherent structures synchronized by the acoustic forcing in the outer shear layer of the swirling flow. These small differences in flame response lead in turn to a misprediction of the FTF at specific forcing frequencies.