Premixed CH4/O2/CO2 flames (oxy-flames) and CH4/air flames (air-flames) were experimentally studied in a swirl-stabilized combustor. For comparing oxy and air flames, the same equivalence ratio and adiabatic flame temperature were used. CO2 dilution was adjusted to attain the same adiabatic temperature for the oxy-flame and the corresponding air-flame while keeping the equivalence ratio and Reynolds number (=20,000) the same. For high equivalence ratios, we observed flames stabilized along the inner and outer shear layers of the swirling flow and sudden expansion, respectively, in both flames. However, one notable difference between the two flames appears as the equivalence ratio reaches 0.60. At this point, the outer shear layer flame disappears in the air-flame while it persists in the oxy-flame, despite the lower burning velocity of the oxy-flame. Prior PIV measurements (Ref. 9) showed that the strains along the outer shear layer are higher than along the inner shear layer. Therefore, the extinction strain rates in both flames were calculated using a counter-flow premixed twin flame configuration. Calculations at the equivalence ratio of 0.60 show that the extinction strain rate is higher in the oxy than in the air flame, which help explain why it persists on the outer shear layer with higher strain rate. It is likely that extinction strain rates contribute to the oxy-flame stabilization when air flame extinguish in the outer shear layer. However, the trend reverses at higher equivalence ratio, and the cross point of the extinction strain rate appears at equivalence ratio of 0.64.