Physics simulators have shown great promise for conveniently learning reinforcement learning policies in safe, unconstrained environments. However, transferring the acquired knowledge to the real world can be challenging due to the reality gap. To this end, several methods have been recently proposed to automatically tune simulator parameters with posterior distributions given real data, for use with domain randomization at training time. These approaches have been shown to work for various robotic tasks under different settings and assumptions. Nevertheless, existing literature lacks a thorough comparison of existing adaptive domain randomization methods with respect to transfer performance and real-data efficiency. This work presents an open benchmark for both offline and online methods (SimOpt, BayRn, DROID, DROPO), to investigate current limitations on multiple settings and tasks. We found that online methods are limited by the quality of the currently learned policy for the next iteration, while offline methods may sometimes fail when replaying trajectories in simulation with open-loop commands. The code used is publicly available at https://github.com/gabrieletiboni/adr-benchmark.