To facilitate the transition from natural gas to a future hydrogen economy, the combustion of natural gas/hydrogen blends in gas turbines will play an important role in power generation. The influence of hydrogen content on technically premixed swirl-stabilized flame using large eddy simulation has proven to be powerful but with high computational costs. Hence, RANS-based models are useful for preliminary investigations and sensitivity studies. Flamelet Generated Manifold (FGM) and Eddy-Dissipation Concept (EDC) are two widely used RANS-based combustion models. EDC, in particular, accounts for the interaction between chemistry and turbulence using detailed chemical mechanisms, but at the cost of higher computational resources. FGM preprocesses the flamelet as a function of mixture fraction and progress variable and pre-integrates the chemistry-turbulence interaction into a Probability Density Functions (PDF) table, which makes FGM computationally inexpensive. This study aims to compare the predictions of these models with experimental data of a methane-fueled technically premixed swirl-stabilized low-pressure burner. The better-performing model is used to evaluate the influence of methane and hydrogen blends (up 40% by volume) in a higher-pressure burner also validated with experiments. The study has shown that EDC produces better agreement with the experimental data than FGM in estimating the flame temperature, flow velocity, and carbon dioxide profiles. FGM did not correctly capture the flame pattern and overestimated the reaction rate. This is possibly due to its simplified preprocessed chemistry mechanism, which could not evaluate the local thermal properties of the gas mixture properly. For the higher pressure evaluation at 5 bar, the EDC model captured the influence of hydrogen content addition on flame behaviour. As the hydrogen content increased, the chemical reaction rate increased, and the flame length indicated by OH decreased. This reduction in flame length is consistent with the experimental results. The CFD showed that at 20% H2, the change in NOx emission compared to 100% methane is negligible using the mass of NOx per unit of heat release calculation. A slight increase in NOx is shown for the same case using the concentration by volume corrected to 15% O2 approach. Nevertheless, both approaches showed NOx reductions at 40% H2. This study has shown that the behaviour of a technically premixed swirl-stabilized flame-firing methane/hydrogen blend is well represented by a non-adiabatic RANS-EDC model with low computation cost. This confirms its applicability in evaluating acceptable lean premixed burners characteristics for gas turbines.