I didn't think any "heavy" shot was softer than lead. The big advantage over lead, at least from what I understand, is that the "heavy" shot is denser, heavier, and harder than lead. By virtue of its hardness it doesn't deform when compressed in tight chokes like lead does, leading to fewer flyers.

I apologize if I'm wrong about this and, if so,wouldn't mind being corrected to learn the true story.