I had a HH Stingray which I traded for my current H Stingray. I too thought the HH would be more versatile, but I was let down by the other sounds. I'm pretty sure the bridge pickup is in the same place as a normal Stingray, but it seems tamer than the single pickup model. Soloing the neck pickup gave an even further watered-down Stingray sound, rather than being Precision-like. The coil tap settings sounded decent, but were very similar (basically a Jazz tone, and a more mid-scooped Jazz tone). The center "all coils on" setting was just a muddy mess.
If I had to go for a two pickup model, I would go for the HS. The single coil neck pickup would give a much more usable Precision-like tone, you'll get a Jazz-like tone from one coil-tap position, and a single-coil bridge setting from the other (since the corresponding neck pickup is underneath the pickguard or a phantom pickup, so it won't pick up on the string).
Also, you already said you're going for a Stingray so this won't apply, but Sterlings and five string HH pickups are wired in series, not parallel, which would give you even less of the classic Stingray sound.