I've not heard of Birth Arts. On one hand, certifying through a better known organization is helpful when you're starting as a doula - folks who go through DONA get more business because DONA is the first place most people look for doulas. That being said, I got all of my early clientele through other doulas' referrals, and it didn't matter if I trained with them or was in the same org as them. If this place has training and a mentality that you like, go for it. I also have heard good things about ALACE, but I don't know if they include herb stuff in their training. Really, once you establish your practice, I think professional affiliation is less important than local connections and reputation. Parents don't necessarily care if you're certified unless you're very new to doula work. The GOOD thing about a certifying org that is really well-known and active is that it offers a lot of opportunities for professional development: conferences, further certifications, etc. DONA has great conferences, as does CAPPA, and there's a lot of room to grow in both orgs.
I certified through CAPPA and it was fine; they're a pretty straightforward group that doesn't do herbal work, aromatherapy, or any kind of exam-type stuff. I'm comfortable with that. If you think you'd like to be more hands on as a doula, I would definitely find an org that will support that, because CAPPA/DONA have policies specifically prohibiting doing those things.
Lauren (33), writer, recovering academic, WOHM to a highly sensitive child (Robin, Feb '08) and mellow little Holly (Jan '10). Newly diagnosed Bipolar I.