Kevin, saying "it depends on the mission" does not answer the question. When was a 12lber better than a 6lber? Was it better enough to justify the extra burden on labor, logistics, manufacture, and finance?
We do not know and may never know. Technical questions can be tricky. The British fought the whole Great War with naval gun propellant that exploded when flashed. It was fixed with a simple chemical reformulation after the Armistice.
I'm willing to concede, that France, the most affluent nation on the Continent, probably had a better educated cadre than the rest, despite the drain of the Revolution. But it seems equally obvious that the artillery curriculum was aimed at producing technologically astute officers, not better gun layers. Drawing might help the production of artillery, but it did nothing on the field, and Russia did not seem to have a problem with manufacting a lot of guns.
Napoleon may have said he could do all those things, but he never did, nor ever needed to. In fact, apart from his competently conducted siege of Toulon, he soon was on to bigger things and hardly had expert experience with artillery.