Why Ferrite mixes have much higher initial permeability (typically in the hundreds or thousands) than powdered iron mixes (typically under 100). Since inductance rises with the core's permeability (L is proportional to mu times N squared times the A-L factor), a higher-permeability ferrite gives far more inductance per turn, so fewer turns are needed for the same value. That is why ferrite is favored for broadband transformers and chokes where compactness matters.
Watch out The temperature-stability claim is backwards: powdered iron, with its distributed air gap, is the more stable and higher-Q choice, which is why it dominates in tuned circuits; ferrite's permeability drifts more with temperature and drive level.
Ferrite = Few turns (high mu). Powdered iron = more turns but better stability.