Steady Laminar Flamelet Model (SLFM) calculation is performed to compare the turbulent combustion characteristics of air combustion and oxy-combustion with $CO_2$ recirculation. Radiative heat loss is considered by the optically thin limit assumption. For more realistic simulation the first-order conditional moment closure(CMC) model is applied to SANDIA PILOTED FLAME D again for the oxidants of air and mixture of $O_2$ and $CO_2$. The chemical kinetic machanism for methane is GRI Mech 3.0. Results show that oxy flames are much more stable than air flames, while comparable stability is maintained with 65% $CO_2$ recirculation. The comparable peak temperature is maintained with 80% $CO_2$ recirculation. Higher the temperature, higher the fractions of intermediate species, CO and OH, due to dissociation.