Body wash tends to contain much more irritants, perfumes, dyes and chemicals because chest/back tends to be more resilient to those chemicals. However, if you have acne, it's not a good idea to use these commercial body washes.
I'd suggest continuing use of the face wash on the chest and back; everything else you can use a normal body wash for, unless you have breakouts elsewhere. If that bothers you...hm...I don't know, tough cookies? I mean, I don't particularly like applying a 4-step regimen every night and spending hundreds of dollars on products, but if it gets the job done, well it's worth it. Make sense? If it's not worth it to you, then just use regular body wash and keep the breakouts. Pretty cut and dry cost-benefit analysis.
BTW, face wash is essentially a gentle body wash. It's probably the best thing you can do for any chest/back problems.
Cetaphil Body Wash, best gentle wash out there.
I'd believe this.