You really are like a dog with a bone aren't you
Speak to anyone who actually rides off road and they will assure you that the AT is not an off road bike and nor is the GS. They are both too big and too heavy especially for mere mortals .
Capable of leaving tarmac? - yes , and are there some amazing videos of both bikes doing pretty amazing things off road in the hands of extremely talented off road riders who, mostly , don't actually own the bikes they are punishing. Ask them if they would prefer to be riding a KTM690 or something smaller then would say Hell YES ! However, they are both most definitely road bikes and very good road bikes at that.
You said it in your later post . The GS is the better all rounder for YOU . That does not make it the better all rounder for everybody.
Also why did you say "adventure looking" instead of an adventure bike . If, like you suggest , it has more of an off road bias than a GS then it's surely a better adventure bike than the GS and therefore not just adventure "looking" ? Many BMW fans looking for a true Adventure bike lament the fact that they can't buy something like an XChallenge just as many KTM riders wish they could buy a KTM690 Adventure. The big bikes are just getting too big. Witness all the GS owners saying that an R9T it way too small , not it's not , it's a proper sized motorcycle.