High fidelity methods to simulate high speed turbulent combustion are of interest to the advancement of hypersonic air-breathing propulsion systems. These methods need to be cost-effective and efficient in order to be of practical use. To this end, we seeks to compare and contrast the performance of two combustion modeling approaches that may meet these criteria. The two turbulent combustion modeling approaches are the flamelet progress/variable (FPV) and the evolution-variable manifold (EVM). Both models use tracking variables to reduce the dimensionality of the species transport equations. As a test bed, both models will be utilized to simulate a reacting transverse jet in a supersonic crossflow. From the preliminary results, we compare OH-PLIF signals obtained from the experiment and simulations. We observe that both models exhibit similar burning regions. However, the flame structures from the EVM simulations resembled more the experimental results. For this version of the FPV model, a more sophisticated compressibility correction is needed before a complete comparison can be made.