Please, the idea that a Sorcerer King knows more about magic and is more powerful then Elminister, even a nerfed 5e Elminister is crazy, SKs are glorified magic scavengers, in a Spell Dual, Elminister would slaughter the SK, because while the SK is draining flowers for magic, El is drawing upon the weave and Mystria. And that is before you count the other two Archmages.
Well depends, in FR I'd say Elminster wins because a goddess has his back if everything else fails.
Alone in Athas? No way. The sorcerer king would drain Elminsters lifeforce to power spells cast at Elminster.
Also a sorcerer king is a level 20+ psionic. Elminster has not enough defenses on his side to counter this.