I get spice from most all my smokes. It's because I like it, and it's what I seek out.
It's sort of the flavor from spice jelly beans that ends up in your sinus. Not the taste (which I hate) but the nuance in my sinus.
Pepper is just that.
I can pick up Black Pepper and White Pepper in cigars.
I don't care for either, but I can tolerate white pepper whereas I absolutely hate cigars that leave a black pepper in my sinus, like DPG Blacks, for instance.
If you've never tried white pepper, it's on most tables at chinese restaurants. It's just like Black Pepper without a smell.
That's my take, for what it's worth.