We have developed a Bayesian version of our likelihood-based Markov chain Monte Carlo genealogy sampler LAMARC and compared the two versions for estimation of theta = 4N(e)mu, exponential growth rate, and recombination rate. We used simulated DNA data to assess accuracy of means and support or credibility intervals. In all cases the two methods had very similar results. Some parameter combinations led to overly narrow support or credibility intervals, excluding the truth more often than the desired percentage, for both methods. However, the Bayesian approach rejected the generative parameter values significantly less often than the likelihood approach, both in cases where the level of rejection was normal and in cases where it was too high.