My Stingray is a four string single H model, so it's not a strictly heads up comparison. But, when I bought my Dimension HH V I played it head to head with a Stingray HH 5. The Dimension seemed more versatile to me, the Stingray a tiny bit more comfortable, but not much.
I played them both through an Ampeg Classic and the Stingray sounded like a Stingray, not a bad thing at all. The Dimension does not have as distinctive of a voice to my ears. You won't hear it on a recording and say, "That's a Dimension!" On the other hand, it can sound a good bit like a P-bass, a Jazz bass or a Stingray with some knob twisting. It will not sound exactly like any of them of course, but it can cover a lot of ground.
As always, your mileage may vary...