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Neither a BP or jacket BC has an overwhelming advantage for single-tank recreational diving.
A BP/W trades the ability to be stable in any position for extra stability when horizontal. Chocolate or vanilla. It's your choice, but there's no real advantage for either.
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The first statement may be true to an extent. They are both BC's and both can be used for recreational diving.
The second statement isn't descriptive of the differences between the two or indicative of the reasons one may have for choosing between the two.
You can achieve trim regardless of what BC you use.
Traditional BC's however usually have excess padding requiring additional (unnecessary) weight to offset this.
In most cases your tank will not be nearly as stable with a jacket style BC as with a BP with a crotch strap.
With a jacket style BC you generally end up with useless straps (chest strap) and dangling straps with rings on the ends (shoulder adjustment straps). You get a bunch of plastic buckles, cummerbunds, pockets you can't get to and in general it just doesn't seem like a traditional BC was ever designed by an actual diver.
With a BP/W it's helpful to have pockets on your drysuit but you need them less since you can now attach a backup light to your shoulder harness since it no longer adjusts for each dive. Since you have a useful waist belt rather than a cummerbund you can attach a cutting tool.
It's easy to have less clutter with shorter hose lengths on the inflator hose and with a waist D-ring you can have a shorter SPG hose. One piece webbing and you can adjust and replace anything about the whole system.
With a SS BP you can take weight off your waist. Keeping the tank closer to your body results in a more stable feeling as well.
There's nothing really tech about it. Switching wings isn't really the big feature some make it out to be since most people don't actually switch wings out all that much.
For most people I believe it's just a better system.