Quartz
Hero
You don't make comparisons between fighting styles using simple weapons, because every class that has a fighting style also uses martial weapons.
That means you compare using greatsword/maul, greataxe (if die size is a concern), glaive/halberd (if using PAM), longsword/battleaxe/warhammer (for sword and board), rapier (for finesse) or shortsword (if light). The other weapons exist for simulationist concerns or niche use cases, and aren't really useful in a balance discussion.
Well, if you substitute shortsword for spear, then you must grant my argument. But I disagree about niche uses. The spear was the standard weapon from the peasant to the noble. And you are not using a polearm or longsword in a confined space - they need room in which to be wielded. But if you run the numbers for a d8 weapon like the battleaxe, the duellist doesn't do that much better - 0.65 damage per attack - which still makes the dual wielder presented in the OP overpowered. Drop the +1 AC bonus and it's just about okay. Or mandate the use of the Bonus Action.