I looked into them once (as a business, not a complainant), and was surprised to learn what BBB was really about. I always assumed they were a pro-consumer advocate, fighting for the little guy, the underdog, the victim. Nope. They're a private, for-profit entity. They take money from the very companies they're suppose to be watchdogging, in the form of "membership." Companies get their "BBB rating" by paying dues. Consumers pay nothing to the BBB. You can figure out from that how their system really works, and who they will protect first when it comes down to it...
Better relief from wrong doing by contractors comes from the state contractors board, though they don't actually have any real jurisdiction over contractors, in terms of punishments they can meter out. They have some leverage, but don't even make public complaint filings. They are, at least, an advocate of the consumer because they are not paid by contractors (not directly, anyway). Contractors pay license fees, but boards get their funds primarily from the state (which are your taxes).
Social media is a path, but just so-so in effectiveness. Yelp is more like BBB, in that they are more into advertiser dollars than integrity. The more you pay them, the better your good reviews stick. There are too many stories of them cleansing accounts of five-star ratings, under the guise of suspicious reviewers. Once you start advertising, your reviews take on a new life.
The only real recourse a consumer has is the judicial system. The double-whammy is the board and the court together. If you can get a judgement from the court, then the board can suspend a contractor's license until they pay. In effect, you can put a contractor out of business until they make good. That's why I always recommend filing a board complaint along with a lawsuit. A judgement is meaningless if you can't collect. A contractor's license at stake is a powerful incentive.
That's all CA, by the way. Other states may or may not have similar protections.