Moon Knight vs Black Panther:
First, while I could argue that "Avatar of the Panther God" is jumping way ahead of known information, it actually does kind of sort of fit with the available evidence in the movies. Maybe this is why Bast didn't show up at the conclave, she has plenty of other business to worry about.
As for the fight? As things currently stand I'd say its either a stalemate or an eventual Black Panther victory. When powered up, Moon Knight seems to have physical stats in the same general ranger as a super soldier, putting them on even ground. He clearly has some form of regeneration, but while its potent its also not infinite or casual; ordinary people with ordinary spears were able to greatly hinder and borderline immobilize him until he gained a burst of "My love interest is about to die" adrenaline. His costume and weapons have some magic tricks, but I wouldn't put them as anything categorically beyond T'Challa's tech gadgets.
Basically, the key thing to my eyes is that T'Challa's durability is just flat out tanky, thanks to all that vibranium in his long johns. Moon Knight, by contrast, may be able to shrug off damage, but he generally needs to take and suffer from it first; that's a notable disadvantage versus an opponent with vibranium claws and supersoldier strength.