Turbulent premixed flames observed in combustion devices exhibit the presence of multiscale and nonlinear turbulence-chemistry interactions, which make predictions using large-eddy simulation (LES) extremely challenging. In this study, two well-established chemistry modeling paradigms, namely, finite-rate chemistry (FRC) and flamelet generated manifold (FGM) are compared using the same computational framework to assess their predictive capabilities. The classical FGM-based framework for LES is extended further by using it in the linear eddy mixing (LEM) model for the closure of the filtered source term for the scalar field. The assessment is performed using two computational setups, a canonical configuration of a freely propagating methane-air turbulent premixed flame, and a practically relevant swirl premixed combustor, both in the thin reaction zone regime, where the focus is to examine the effects of chemistry modeling paradigm and SGS turbulence-chemistry interactions. While for the first setup, direct numerical simulation (DNS) is considered as a reference for comparison of different models, for the second configuration, the results are compared with the available experimental data. Overall, while mean flow features are predicted reasonably well by the FGM-based approaches, quantitative differences are observed for intermediate species and conditional statistics when compared with the FRC-based approaches, and possible reasons for these differences are discussed.