The BH and AD

I am no expert, but I have put the BH on Gracie twice now -once via USA SchH, and once via AKC Working Dog Sport (AKC assigns it the TT title).  They use identical procedures. 

Once you qualify your dog with the BH, there is no need to re-test.  (The only reason why we have "two" is that AKC does not recognize the BH.)  The expectation of precision and high attention to handler is similar btwn both USA SchH and AKC Obedience.  But the easiest difference to identify is that with the BH, it's PASS or FAIL.  That is it.  Same for WDS TT. You never know what your "score" is.  With Obedience, if you don't NQ on a section, you will be given a score, etc.

Have never done the AD - Gracie just isn't meant for endurance sports like that.  (Particularly in the blazing sun of AZ)  I think a properly conditioned GSD should be fine.  If you google SchH AD, there's a conditioning plan on siriusdog.com that you might find useful.

I have heard that as for the actual heeling, a sloppier heel (relative term, even the "sloppy" SchH heel is pretty darn good) is often more acceptable in SchH than AKC obedience, but attitude and willing attention to the handler is more prevalent in SchH.  Is that true?  Do you see it at the BH level?  I don't know if this was in reference to the BH, or the SchHI, II,... tests.  I've only seen SchHIII tests and high level competitions on YouTube, but I can see where the heeling is different than AKC obedience.  I've seen AKC obedience in person, and it seems a lot of the dogs look sort of "checked out" and are just moping along behind the handler, whereas in SchH it seems the dog must demonstrate a very focused and energetic attitude.  I was also told that say for instance you are calling your dog in SchH and when it comes to the front sit it was running so fast and is so excited about this recall that the dog skids into you...in SchH that would not be surprising but obviously in AKC obedience that would be penalized b/c the dog didn't make a nice easy stop right in front of you.  Hearing things like that actually make me MORE interested in SchH style obedience b/c my main focus has been Kenya's attitude, confidence, focus, drive, intensity, etc...not necessarily perfect precision.

Liesje

obviously in AKC obedience that would be penalized b/c the dog didn't make a nice easy stop right in front of you. 

Actually, I don't think that's the case.  Our training partners have most of the same titles as Gracie does, and she earned her second leg of her AKC CD last week.  The dog came flying at her (as she does regularly due to BH training,e tc) and slid to a stop in front.  The judge actually commented on the enthusiasm - and no deductions.  In fact, they earned 3rd place.

The attention is VERY important in SchH, but in all honesty, what the judge will pass in BH could be considered "easier" than AKC Obed.  In SchH, looking like a working team, with the dog being an eager partner, obedient and attentive, is very important.  The judge literally makes a judgement if your overall performance shows that the dog is willingly and eagerly obedient to you without any extra "help" from you.

The day Gracie and I did our "second" BH, she was focused on me enough to pass, but nothing like the level I'd expect of her.  It was ungodly hot for October, and we'd barely trained a lick as I was prepping for my move across country.  I don't think her heeling would have gotten particularly good scores in AKC Obed.