Frozen where texture and colour matter and you have freezer capacity; dried where shelf stability, transport cost or a dry application decides. The honest comparison is delivered cost per kilogram of finished dish, not price per kilogram of raw material.
Why it works this way
Freezing preserves the cell structure far better than drying does. An IQF mushroom thaws close to its original texture, and the colour is held by the blanch step that precedes freezing. Drying collapses the structure, and rehydration recovers only part of it – noticeably less in a fibrous species such as chanterelle than in a boletus.
Drying wins everywhere else. A dried mushroom is roughly a tenth of the weight of the fresh material, so transport cost per kilogram of dry matter is a fraction of the frozen equivalent, and there is no cold chain to maintain, no reefer to book and no excursion to argue about. Shelf life is measured in years rather than months, and a dry ingredient can go into a dry mix, which a frozen one cannot.
The cost comparison is therefore not obvious. The dried product carries a rehydration yield that has to be accounted for; the frozen product carries the cost of moving and storing water.
What follows in practice
Run the arithmetic on your own application: dried input weight times rehydration ratio against frozen input weight, plus your storage cost, plus freight. Then check the texture outcome with a trial rather than assuming it.
The IQF champignon record and the dried porcini record set out the specification differences that follow from the format choice.