Neither.
HS.
I currently own a single H, its a short scale though. And I recently got rid of an HS. I also have an HS Sterling 5, and an HS Bongo. I have owned 2 HH Bongos (a 4 and 5 string).
HH, to me, was less versatile than the HSs, and to a certain degree, overkill. The bass is aggressive a $%*, and for me doesn't need any more. If anything it could use taming, and the single coil pickup did that for me (and still does on my other HSs). Musicmans don't typically have many Fender characteristics, but I feel I can get them to do that with the HS when I start turning the EQs down as opposed to up. On all my MMs I now consider about 1/3 of the way up (like #3 if they were numbered 1-10), flat. When I start EQing from there and using my volume to adjust, I get a billion awesome sounds. Sounds I never thought possible before I got comfortable doing that.
Anyhow... yeah. HS is my preference. It gives that extra slapping space at the neck too, not that I really missed it with the HH.
Just saw @Killing Floor 's post and realized I forgot the mention that I'd definitely go with a double pickup, no matter what. On my HS I don't even know if I ever soloed the bridge pickup. There is a LOT more depth as well as some super funky and syrupy sounds with both pickups kicked in. It doesn't ever lose the Stingray tone, just kinda adds to it.