To ME, as a casual, vacation recreational diver, the best feature of a BP&W is that it can be endlessly adjusted. Meaning I can gain or lose weight, change from a thin wetsuit to a thick one, or even lend it to a friend, and the harness can be endlessly shortened and lengthened as needed, so it always fits (plus it doesn't squish my boobs but I guess that won't be an issue for you).
Fit is very important in a BCD, because if it's too tiny you can't use it at all. And if it's too loose, you can't keep your balance in the water, as the BCD which holds your tank will slightly shift and you'll be rolling left to right. Very uncomfortable.
While vest style BCDs can be adjusted somewhat, there is not much leeway. Go from a 1mm wetsuit to a 14mm or dry suit, gain or loose 20 lbs, and your once perfect BCD may not fit you.
Another perk I love is that it can be entirely taken apart (especially the Deep Sea Supply one, where it takes a few seconds to separate the wing from the plate), so it's super easy to rinse, store and travel with.
Vest BCDs tend to be bulkier (depends on the model, though).
Also, because of their design, BP&W are very streamlined (no excess drag and volume), so you won't need as much lead to submerge (we're talking a few pounds here, not 20 kg).
The streamlined design means less drag in the water, so less finning.
The back inflation (which is also available in some vest-style BCDs) helps achieving better trim (being horizontal in the water), which also reduces drag.
Since the plate (which is usually made of steel, some are built in less dense material such as kydex for people who don't need extra weight to submerge) and the wing can be separated, it also allows one to buy different types of wings to adapt to their diving needs (for exemple, a small wing for tropical diving when you don't need a lot of lift, and a big wing to dive with thick or dry exposure suits, as those require more lead to submerge).
Note that a BP&W is typically designed for those who dive with double tanks, which is why many designs require that you use a single tank adapter (STA) if diving with a single tank. (that's one of the reasons I went with the Deep Sea Supply design, it doesn't require a STA, as I have no desire whatsoever of diving with double tanks).
Finally, a BP&W can be customized to your own needs, by adding D rings anywhere on the harness wherever you want them to attach your gear (SMB, whistle, lamp, weight pockets, whatever). Those rings can be removed, put somewhere else… so the kit pretty much grows with you.
The backdraws of a BP&W according to some people are :
• they are a bit harder to get into (you adjust the harness before you don it, whereas a vest style BCD can usually be loosened before donning and then tightened). Haven't found that to be an issue.
• they tend to "push you face down" while on the surface. In my (short) experience, this is true if you fully inflate it. If you just inflate it enough to float, not an issue, just lean a bit backwards and problem solved.
• some people enjoy the "safe feeling" of being envelopped by a vest jacket. I'm the opposite, having something inflated around my stomach or chest area makes me feel "squeezed" and uncomfortable. To each their own.
• a BP&W harness usually has a crotch strap (a piece of harness that hangs in your back, goes in between your legs and attaches to the front). Some guys find that uncomfortable (not being a guy, I obviously don't have that issue). That strap really helps in keeping the BP&W and tank in place (with vest style BCDs, my kit would "ride up" every few minutes, and I'd have to pull it back down). That being said, I've read of several people who never had that issue and of BP&W users who just got rid of the crotch strap. Again, to each their own.
You'll find more arguments about the pros and cons of both types of BCDs in the equipment forum. I tried to be as objective as I could, but as you can see I'm pretty sold on the BP&W…