This paper addresses the Bayesian hypotheses testing for the comparison of exponential population under type II censoring. In Bayesian testing problem, conventional Bayes factors can not typically accommodate the use of noninformative priors which are improper and are defined only up to arbitrary constants. To overcome such problem, we use the recently proposed hypotheses testing criterion called the intrinsic Bayes factor. We derive the arithmetic, expected and median intrinsic Bayes factors for our problem. The Monte Carlo simulation is used for calculating intrinsic Bayes factors which are compared with P-values of the classical test.