Griffo
Contributor
BP/W is an abbreviation for "backplate and wing". The backplate is a plate (usually aluminum or steel, but sometimes plastic) with slots for a harness and holes and slots for tank mounting hardware. The wing is a an air-bladder that attaches to the backplate.
Another style, which you've probbaly seen, is a "jacket" BC, which is mostly fabric, with straps to mount the tank and usually some sort of internal plastic frame to help hold the tank.
SCUBABoard has a very vocal BP/W fanclub, however if you're doing recreational dives you won't actually find a lot of BP/Ws out on dive boats, and you'll seldom see them in a dive shop.
There's nothing wrong with it, however unless you need a place to bolt 100+ Lbs of tanks, there's no huge advantage either.
Just like everything else in SCUBA, it's a bag full of compromises, and the only way to know which style you actually prefer is to try both.
flots
Not sure if you noticed this thread is kinda old. But anyway, in my local area, BP/W's would outnumber jacket BC's at least 2-1 on most boat trips. All the LDS now stock plates and wings, the last hold-outs to the old business models have even brought in Scubapro models, although the big H and Hollis seem the dominant brands. I have theories on why, but it's just how it is.
Having said that, I went on a live-aboard last year less than 300miles from home and everyone was asking me why I was diving tec gear..