Weight and weight distribution is one thing, but stock design is another very important feature in shootability. This is somewhat subjective, but the hooks on a butt plate as in a plains rifle will not help much or at all if the rifle doesn't fit you to a tee with whateveryou happen to be wearing. In other words, I find those butt plates with curved crescents need to be close to a perfect fit, than a flat butt plate . Flat butts help in this regard due to ones ability to move the shoulder forward easily with a butt that fits into the shoulder's pocket, not in the pit or out on the arm and thus, bring the eye in direct line with the sights.
English designs excel in being 'shootable', not only on target, but being quick shooters for hunting as well. Jaegers also fit well for target and sporting purposes, almost as well as an English hunting stock design. My English designed 14 bore is a good expample. With it's 30" barrel of .69 cal. at 9 1/2 pounds, it's weight is perfect for absorbing recoil, which long range (past 50 yards to 300 yards) requires - ie: heavy charges are needed for longer range shooting and with a narrow butt, especially a Hawken type, there are limits to bore sizes before recoil becomes painful. It is also light enough to allow packing all day, and swings like a slightly heavy upland gun.
The larger the bore, the better is the long range accuracy, all else being equal. Stock design is very important here. I would no sooner shoot a 9 1/2 pound Hawken in .69, with my hunting charges, than someones 4 bore single. Not going to happen, yet the English cap-lock design is very comfortable to shoot. The heavier ball is less effected by the elements & therefore is more accurate. Prime amongst the elements, is the one of consistency in the ball itself. The larger the ball, the more inconsistencies it can have and remain just as accurate, or more accurate than a smaller ball.
Reasonably good casting quality with a minor defect in a larger ball can reward the shooter with remaining exceptional accuracy, whereas the same defect in a smaller ball can more greatly effect the accuracy and cause fliers.
Barrel weight and gun balance are only 2 aspects of the shootability of a rifle - or smoothbore for that matter. Design and fit are 2 more very important traits that must be studied.