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Common knowledge tells us that a large air coil will have low loss compared to a toroid core coil but this may not be the case. Consider three factors: the length of the wire, the capacitance between windings, and the hysteresis loss in the core material all can increase loss but the addition of a core loss for a toroid coil could be offset by the fewer turns needed for a given inductance which reduces the loss in the winding and the interwinding capacitance to the point where the toroid coil could have less loss than the air core coil.
Speculation, being what it is, solves nothing but it does point the way for experiment and questions. I have seen reports of Q factors for powdered iron core coils as well as for typical air core coils which suggests that the powder iron core loss is less than that for air coils. A good experiment as Robert suggested would be interesting.