I don't own the HD (I've only heard it in clips), but I do own the CS and know it very well.
They're quite different; HD is Alnico V and the CS is ceramic. HD pushes more mids, whereas the CS has it's mids more neutral. HD has a warmer top end, CS is much sharper (but not harsh).
The CS is an absolute beast in a warm and middy guitar; it's thick and articulate aggression with the CS. I own a maple topped alder strat, which happens to be quite bright and has a slight scoop in the mid mids (maple top does that); I definitely wouldn't put the CS in it. But if I wanted to replace the NB, the HD would work wonderfully in that guitar. Actually, I just might do that at some point, just to satisfy my curiosity :)
-Zaned