From what I can tell, the classification of a soft vs hard magnetic material is more of an engineered property.
To put it simply, elements have various levels of being able to be magnetized and to hold onto that magnetization. Magnetization is caused by spinning electrons.
Materials with complete shells have electrons spinning in both directions in each shell, thus the magnetic effects cancel and are not as magnetically interactive. Most common magnetic elements have outer shells not complete, with more shells with single electrons, that create the 'uncanceled' dipole moment (FE, Ni and Co). If these material are exposed to external magnetic field, these dipoles align and persist. (Side note - interesting I am guessing its not likely to find many 'pre-magnetized' magnets in nature).
Back to the hard and soft, doing some brief searches, it appears hard magnets (like speaker magnets) are more pure forms of these elements, and would expect that crystalline structure of the material is made to optimize the magnetic effects. The soft magnetic material (like power transformers) are again the material than can be magnetized, but infused with other elements to reduce the ability to retain the magnetization (silicon steel was a term that came up). Hence, why it appears to be more engineered properties than elemental properties.
So, while the number of available dipoles is a factor, it looks like it could be how much they are able to interact is a significant factor. This input only came from a half hour review of an old material science text book, for what its worth.