We study the simultaneous message passing model of communication complexity, for the case where one party is quantum and the other is classical. We show that in a protocol where the first party sends q qubits and the second party sends c classical bits, the quantum message can be replaced by a randomized message of O(qc) classical bits, as well as by a deterministic message of O(q c log q) classical bits. In particular, our results imply that quantum-classical protocols need to send Omega(\sqrt{n/\log n}) bits/qubits to compute equality, and hence are not significantly better than classical-classical protocols (and are much worse than quantum-quantum protocols such as quantum fingerprinting). This essentially answers a recent question of Wim van Dam. Our proofs rely heavily on earlier results due to Scott Aaronson.