  We present an in-depth study of the problem of multiple-shot discrimination
of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically,
we consider two scenarios: minimum error and unambiguous discrimination. In the
case of minimum error discrimination, we focus on discrimination of
measurements with the assistance of entanglement. We provide an alternative
proof of the fact that all pairs of distinct von Neumann measurements can be
distinguished perfectly (i.e. with the unit success probability) using only a
finite number of queries. Moreover, we analytically find the minimal number of
queries needed for perfect discrimination. We also show that in this scenario
querying the measurements gives the optimal strategy, and hence any possible
adaptive methods do not offer any advantage over the parallel scheme. In the
unambiguous discrimination scenario, we give the general expressions for the
optimal discrimination probabilities with and without the assistance of
entanglement. Finally, we show that typical pairs of Haar-random von Neumann
measurements can be perfectly distinguished with only two queries.
