I use both balls. My Black Diamond is not near as strong as my Sting WM. The shot shape is also very different. The BD has a very angular shot shape, very hard off the friction with little read of the heads and only a little of the midlane. Very unusual for a solid particle ball, but I have to say it's the most angular ball I have used from Lane Masters including the original Buzz. The Sting WM is one continuous hook to the pocket. Nothing fancy, just one big arching move from around the end of the heads, through the mids with a nice pop off the friction.
For me, the Sting WM is better for heavy or longer oil than the DB, with the DB really showing its stuff when the shot starts to break down or there is a bit of carry down and you need that extra recovery at the break point. The Sting WM works best on fresh as it seems to temper down the effects of over/under where the DB can make it much worse, depending on how much hand you have.
Your mileage may vary!
Just a mention, I should have the Black Diamond Particle Pearl this weekend.