That is your opinion that the French were superior even in 1813-15. The Grande Batterie was a blunt weapon. The innovative and effective use of French Horse artillery up to 1807 was a thing of the past. The failure of the horse artillery to support the failing quality of French Cavalry. The Grande Battery was not the great barrage of the WWI that so shaped the writing in the 20th century. Artillery was nowhere as effective as in ACW which could be considered the first of the modern wars and a few years later the Franco-Prussian War.
Experience was important and the aggressive commanders had been killed. The French Artillery Manuals are silent upon battery maneouvres let alone of more than one battery. The first manual that talked about this was in 1824. All the previous were upon a pair of guns and 4 guns at best.
Artillery is a component in a battle winning formula. It cannot and did not win the battle alone. This is much akin to airpower being able to win a war on its own.
The structure and flexibility of the Prussian System survived into the 20th century but the French system did not. The organisation of three was a very successful organisation.
It is very difficult to sort out precise effects from the reports of battles. This becomes very subjective. As you were a serving officer, you understand that time is a flexible medium. In action time runs quickly. Timing of actions often differ by hours. Watches were expensive and rare. They were no-where as reliable as we consider then or not now.