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Delegated quantum computing (DQC) enables limited clients to perform operations that are outside their capabilities remotely on a quantum server. Protocols for DQC are usually set up in the measurement-based quantum computation framework, as this allows for a natural separation of the different parts of the computation between the client and the server. The existing protocols achieve several desired properties, including the security of inputs, the blindness of computation and its verifiability, and have also recently been extended to the multiparty setting. Two approaches are followed in DQC that demand completely different operations on the clients' side. In one, the clients are able to prepare quantum states, in the other, the clients are able to measure them. In this work, we provide a novel stringent definition of the equivalence of protocols and show that these distinct DQC settings are, in fact, equivalent in this sense. We use the abstract cryptography framework to prove our claims and provide a novel technique that enables changing from one setting to the other. In this way, we demonstrate that both approaches can be used to perform tasks with the same properties. I.e., using our proposed techniques, we can always translate from one setting to the other. We finally use our results to propose a hybrid-client model for DQC.