The drawback of the Williamson over the ACs is the fact the damage is spread out instead of being a point damage weapon. Due to the way armour reduction is calculated, it's far better to have a single high damage projectile rather than higher DPS spread out over fewer shots, as armour 'catches' more damage that way. Further, overload durations are dependent on the strength of the individual shot that pushes it over, so again, having a single high damage shot is better than having lots of very small low damaging shots. This means that, in general and despite the stats, the Williamson is actually an inferior weapon, however slightly, when compared with dual AC. It is supposed to be better than the light AC. I'll check the range though - it's supposed to be slightly smaller than the dual AC's, but I might have mixed up their ranges with the railgun.
The thing is, I don't think the per-shot damage disadvantage matters because it is a much better weapon than both ACs and almost all hulls will give you leeway to fit an actual armour-breaking weapon. The Williamson shotgun not only has good theoretical flux efficiency, but because of its faster projectile speed and its small consistent cone of damage vs the dual AC's single shots at a time with large recoil variance, it has much better practical damage application too. The range doesn't seem to matter that much either, because the ships can't kite very reliably with only a 15su margin. In practice, the shotgun wins flux wars a lot more often, allowing a HE weapon to do the actual damage.
I ignored the 685 as a typo and did my tests with a 585-range Williamson shotgun on Lashers (Lasher variant: ITU, 2x Harpoon, 9 caps/10 vents, flux coil, unspecified ballistic slots get Vulcans) in mission sim (no fleet skills):
2x Shotgun wins flux war vs 2x Dual AC, and veeeerrrry slowly kills it over many many engagements
Shotgun/LAG wins flux war and does damage to Dual AC/LAG each engagement
2x Shotgun + Light Mortar wildly outclasses 2x Dual AC + Light Mortar
The differences would probably look bigger if I optimised the builds for anti-frigate work.
The cases where the dual AC wins are when you can't afford to also fit an armour breaking weapon of any kind on your hull, when you have sparse small ballistic slots that must be used for both shield-breaking and fighter defence so you can't fit a LAG (although IMO the shotgun achieves far more hits on low armour fighters than the dual AC), or when the only kind of HE weapon you can fit are those with a very low ROF, allowing a high armour enemy to bathe in lots of minimal-damage shotgun hits and shield-flicker armour-breaking shots. These don't seem like very likely circumstances outside of odd game situations or very specific hulls.