Not that familiar with AKC/CKC style obedience either, but I would say that a BH is equivalent to a CGC/CD/ and some elements of the CDX.
Having done both, I'd say not really. A dog can not only pass the CD/CDX but get a really good score even if they almost flinch or crawl through the exercises. I find the openess of the SchH field to be a much more difficult distraction then the obviously contained AKC ring, and the group part is pretty easy to practice if you have a few friends with dogs, trained or not. The CGC test, while commendable, is pretty easy to rehearse a pass and have nervy dog get a certificate. I know that it makes sense to have every test be exactly the same because Americans want everything to be fair, but it does lead to a less than true reading of the dog's character in many cases. I was at an fun event a few years back and we had 6 dogs with us, they were doing CGC tests as a fund raiser. We had never done the test but decided to enter ours for the heck of it. Of course ours were all at different levels in their training, but what the heck. They all passed with flying colors and so many of the spectators and testers just gushed over our dogs. We were shocked that they were so impressed at what we considered basic minimum skills.
We also offer dog daycare as part of our business and many prospective new clients feel like they shouldn't have to do the evaluation if their dog has a CGC. We always ask what age they did the test. If the dog was younger than 15mos or so, then we tell them we need to do our own evaluation as the dog has probably matured now and we need to make sure the social skills are compatible with daycare. I am always shocked at how many were done at 7-10 mos. I'm thrilled they took the time to do it, but I am not going to take at face value that the adult dog will react the same way now.
Every GSD in our house (7 at the moment) has Kkl parents. I know it is expensive to do all that, but we have done it with our own and when we bought from other breeders we were perfectly willing to pay what they asked since we understand the time and cost involved.
Granted, we have only been involved in producing 3 litters in the past 10+ years since that is not our "thing".