Thanks for that response. I actually have a Precision Elite and find that the neck pickup, in either active or passive mode, does not really sound like a true new or vintage P-bass. It's kind of its own thing.
When I was considering buying a new Stingray, I was seriously considering the HH for the versatility, though I much preferred the single H aesthetically. But after listening to many demos, was surprised how different the HH sounded solo'd on the bridge. I really like the sound of the SB-1, and the looks. Might have to consider a custom build.
I guess the answer, like always, is to buy one of each.