The wings devotees will argue, but this line from another thread illustrates what is nice about the stab jacket:
"I'm my open water class with a jacket BC I was rolling all around and unstable in the water, with the Halcyon unit I'm planted in a great horizontal orientation."
That's great. But the stab jacket allows me to roll around. That's not a weakness. That's it's beauty. The wings are fine if you want to be "firmly planted in a horizontal", but I like freedom of movement and don't want to be firmly planted in any position. On the wings there is a more noticible shift in air if you roll from side to side than in the stab jacket, because the stab jacket is wrapped around you and the air doesn't have to move as far.
I dive wings on my doubles and they are OK, but I don't want to roll to my side with the doubles anyway. For my single tank, I have a SeaTec and a Scubapro wings BC. I know what wings are like. They are OK, and I dive with them. But for me, the stab jacket allows more freedom of movement, and is more "forgettable", as if I'm not wearing a BC.