The only benefit is size, and involves excessive shortening of the wrong end of the gun due to legal constraints on shortening the other end.
Or when shortening both ends, an AOW is legal in places a short barreled shotgun is not, like California for example. You can have a PGO with a short barrel, but not a short barrel and a stock.
AOW also have fewer rules, like checking in and getting ATF permission to take them across state lines.
Most of the benefits of a PGO are really artificially created because of legal constraints. A short barreled shotgun with a folding stock can be just as small as a full barreled PGO shotgun while being a lot more useful. The NFA keeps them from replacing PGO guns.
Since the current minimum shotgun length without going into NFA territory is 26 inches, and that is right about what many 18 inch barreled guns with typical autoloading and pump receivers are with no stock attached, a PGO is the most common practical way of legally reaching the minimum 26" gun.
However firearms like the KSG should resolve that.
That KSG is also 26" overall, the same length of something like a mossberg 500/590 or Remington 870, and many other common receivers with a PGO and an 18" barrel.
Yet it is clearly superior to a PGO shotgun, while being of the same minimum overall length and barrel length without being an NFA item.
If bullpup shotguns of 26" overall length become commonly available that allow shoulder fire without NFA paperwork then the primary benefit of a PGO non-NFA shotgun disappears.
Then the only purpose of a PGO shotgun would be for even shorter NFA firearms.