So you are saying for a non-focused build that spends feats on both close and long range weapons, duelist isn't as good.11th level Fighter, Variant Human:
Fighting styles: Two-Weapon Fighting, Archery
Feats: Dual Wielder, Sharpshooter
Skills: Stealth, others chosen to taste.
Stats & other feats: Chosen to taste.
The melee/archery approach isn't as strong with Duelist. You choose either sacrificing action economy or sacrificing at least 2 points of AC. It's not trivial thing to ignore, as this is specifically what makes the TWF DEX choice so strong for Fighters. Even with the other subclasses, the fact DEX works for both longbows and versatile melee weapons makes it a strong choice.
There are other effects downstream of having that additional attack. You gain more from magic weapons. You don't sacrifice as much to Shove + Attack. You benefit more from certain spells like Enlarge/Reduce and Elemental Weapon. A Battle Master can potentially spend an additional die (wouldn't recommend for EKs). You're likely to force more concentration checks on casters. You lose less damage potential to overkill. Etc.
But for that build, you are competing with the wrong alternative.
XBE+SS is the same number of feats and gets you a 1d6 weapon usable up to 120' away with a bonus action extra attack, -5/+10 option even in melee, attribute bonus to damage already. And you can mix in +1 bolts (if they are cheap in your world) to get +1 damage and +1 to hit.
You lose 1 AC from DW, which you can make up by taking the defensive style instead as your 2nd style.
And you only need 1 magic weapon, instead of 3. I mean, if you need long range, you can also own a heavy crossbow (1d10) or a longbow with even more range as a backup magic weapon.
-5/+10 and +2 to hit from archery style is hard to compete with with DWer. I mean, DW flametongue rapiers +9 to hit for 1d8+2d6+5=16.5 damage, 4 attacks/round.
An equal rarity +2 hand crossbow with +0 bolts is +8 to hit for 1d6+15=18.5, 4 attacks/round. And doesn't use up 2 attunement slots, and permits magic bolts on top of that, and gives you the +13 to hit/10.5 damage per tap option for high AC foes.
Going +2 on the rapiers instead of flames is +2 to hit for -5 to damage each; 2.5 damage per point to hit. The tradeoff for the XBE is 2 damage per point to hit, making accuracy cheaper for the hand crossbow build, and the hand crossbow can swap on-the-fly on each attack depending on the situation.
The baseline rapiers (no magic) deal 1 more damage per hit; the baseline hand xbow does 2 more to hit.
It isn't very close really.