There is much to do with accuracy and consistency, both in the firearm and the shooter. But the OP was asking about only the rifle, and particularly, about hooked breeches.
As has been stated, a hooked breech must be carefully filed and fitted so there is no movement in it...it must lock up solidly when the barrel is lowered into the channel. Also, the standing breech must be inlet properly so that it is bedded perfectly against the wood of the stock. If there is any gap between the steel and the wood, the tang will be allowed to flex and bounce and that is disastrous to accuracy.
As with the rifles pictured that have no forestock, wood bearing unevenly against the surfaces of the barrel will be problematic. So when a forestock is used, it must be inlet carefully together with the barrel lugs and keys/pins. Provision must be made on the fore and aft surfaces of the keys/pins so that they have no influence on the recoiling barrel, other than to hold the wood against the barrel. Further to that, the escutcheons, if present, are there simply to protect the wood around the keys/pins, not to support them. The keys/pins should have consistent contact with the stock wood, while the slots in the lugs should have clearance fore and aft. With all this in mind, it makes sense that a half stocked rifle should have the potential for greater accuracy than a full stocked one. One item often overlooked is that a rifle will shoot differently if the ramrod is not replaced on every shot. Also, when shooting from a rest, where the rifle contacts the rest and the nature of the rest, affect its accuracy and consistency
Sights and rifle fit to the shooter are two completely different issues.