Jason,
The Big Al was made SSS or H, never made with the HH configuration, as far as I know. I can, however, tell you this: My first year Big Al SSS has an Alder body, Blue metalliac in color, after that the bodies were Mahogany. My Big Al H has the mahogany body, metalliac Burgandy in color. The SSS has about a million sounds, none of them sound like a Stingray, the H has about 3 sounds, to my ears, none of them sound like a Stingray either. Sterling yes, Stingray no. Both play wonderfully well. The SSS is much brighter than the H, however, the 4band EQ can control that, but it can't add what the pickups don't send it. The H is nowhere as bright. I prefer the SSS for sound, the H for it's color. Both are worthy of being "The Best Bass I Own", except that I am a bass whore and I have many basses worthy of being "The Best Bass I Own". Which brings me to the Bongo basses. I have a HH,Cardinal Red metal flake, and a Hp First gen Dargie Delight. Both sound great, play great and look great. I think the Hp is richer and fuller than the HH, but, as I have said before, both are worthy of being "TBBIO". I don't think you can go wrong with any of the Big Al or Bongo basses.
YMMV
Ken R