For non-premixed combustion, the steady laminar flamelet model (SLFM) and flamelet/progress variable approach (FPVA) are two popular methods for tabulating flamelet manifolds. Even if the two methods are used to tabulate and parameterize the same flamelet database, their results sometimes differ in the subsequent simulation. In this work, a novel perspective is provided to assess the performance of the SLFM and FPVA. Both approaches are compared with respect to their capabilities to capture tangential diffusion (TD) of the thermochemical state variables along iso-surfaces of mixture fraction. The relevance of TD effects is identified using generalized flamelet equations and regimes by comparing flamelet solutions with and without TD terms to a FTC (full transport and chemistry) solution of a well-known non-premixed coflow flame. It is found that TD effects can play an important role in entire mixture fraction space, even in the classical flamelet regime. This suggests that the ability to characterize TD effects is an important performance indicator for tabulation strategies. Thereafter, an a priori analysis is conducted comparing the results from the FPVA and SLFM (using the same flamelet database) with the FTC results. The results show that the FPVA is able to more accurately describe the thermochemical state and the flame structure than the SLFM. For a more detailed assessment of the two tabulation strategies, the TD terms reconstructed from the FPVA and SLFM are compared to those from the FTC results. It is found that the FPVA can capture a significant portion of TD effects, while the SLFM can hardly characterize TD effects. This particular capability allows the FPVA to describe chemistry-transport interaction and flame structure more accurately than the SLFM.