Advantages of a traditional BC:
You're used to it, because you most likely trained in it.
Integrated weights.
Pockets -- although they may not be easy to access, or convenient to get things out of.
Quick releases -- easy to get in and out of the gear.
POSSIBLY -- depending on tanks and exposure protection -- may make it easier to float upright on the surface.
Advantages of a backplate and wing:
Infinite adjustability. You can get a perfect fit FOR YOU.
Backplate becomes part of your ballast, reducing the lead you have to carry. It also puts weight up between your shoulders, which encourages horizontal trim.
Absolute stability of the tank.
Front of the body is unencumbered, for improved comfort and streamlining.
Rig is modular, so you can move from cold water to warm water to doubles and all you may need to change is the wing.
Disadvantages of a backplate system:
Need to come up with some kind of weighting system. Options are pockets for the waistband, or a weight belt, or a weight harness like the DUI Weight & Trim.
Need to come up with someplace to store incidental items. Options are pockets on your exposure protection, or X-shorts, or pockets on the waistband.
Lack of releases. Improperly adjusted harnesses can be a PITA to get in and out of.
If you already have a backplate, I'd buy a wing and put the rig together. I don't think you'll be unhappy with it.