The paired comparison models endeavor to compare treatments based on their sensory evaluations made by a set of respondents. Abbas and Aslam (2009) proposed the Cauchy model for paired comparisons using the Cauchy distribution. In this study, an attempt is made to compare treatments and assess equivalence appearing in the treatments through paired comparison, proposed by Abbas and Aslam (2009), is extended to serve the purpose. We perform Bayesian analyses of the extended Cauchy model via the uninformative and informative priors. We use real dataset based on the efficiency of pain-killers assessed by patients. The resulting estimates are obtained using both the priors and are compared. Interesting conclusions are drawn based on the results.