Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic trace-distribution equivalence differentiates systems that can perform the same set of traces with the same probabilities, and is not a congruence for parallel composition. Probabilistic testing equivalence, which relies only on extremal success probabilities, is backward compatible with testing equivalences for restricted classes of processes, such as fully nondeterministic processes or generative/reactive probabilistic processes, only if specific sets of tests are admitted. In this paper, n
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