Upon reflection, we don't have to imagine what would happen if Wellington's army confronted a Southern army. Andrew Jackson settled that question at the Battle of New Orleans. The fire of batteries of cannon did great execution that day. The same thing happened to Bragg's smoothbore armed infantry at Stones River. In any case, history has shown that Napoleonic era tactics & weaponry were obsolete by the time of the Civil War.
I've had a look at New Orleans and the problem was mainly that an experienced battalion of the 93rd advanced to the defences, but then stood in front of them engaging in a firefight rather than storming them. I remain firmly of the opinion that had the 2/93rd made an assault it would have been a bloody victory instead of a defeat.
Technology had advanced, but much of the increased potential was neutered by lack of training. It is unquestionable that the percussion cap increased infantry firepower, and at typical ACW firefight ranges this may have mattered more than the rifling. The percussion cap is far more reliable, and because there is no flash in the pan, you can maintain the sight picture effectively. The effect of rifling though was diminished in line combat (rather than skirmishing) due to the lack of well-trained fire control. That it could be done is demonstrated by Cleburne's Division, but it was not.
For the artillery, the 12 pdr Napoleon came about from French experiments with combining howitzers and cannon into a single weapon (hence the gun-howitzer name). The original experiments were based on bored out lighter pieces (8 pdrs I think) utilising a powder charge between that of a gun and a howitzer of that projectile weight (i.e. 2.5 lbs i a 12 pdr gun-howitzer vs 4 lbs in a 12 pdr cannon). Experiments showed the new weapon had 90% of the effect of a "full" 12 pdr, but could be handled as an 8 pdr.
The rifled guns are more interesting, but the exact combination of shot geometry and weight, rifling and velocity necessary for effective long range fire was not known. What worked was determined during the 1862 campaigns.
The idea that artillery could "charge" in Napoleons time is not borne out by close examination of Friedland. Senarmont was the artillery commander for Victor's 1er Corps. The action involves DuPont's division of 1er Corps advancing to support Ney's corps attack (on Victor's right), but then being stopped dead by a charge of the Russian cavalry. DuPont's division is forced into squares to protect themselves. The divisional battery under Capt Ricci is firing well, but it is suffering by Russian artillery. Victor directed Senarmont to reinforce Ricci with the whole corps artillery. Senarmont did this, and lined up 30 guns just as a Russian infantry division moved to overrun DuPont's paralysed division. These 30 guns broke up the Russian infantry attack very effectively, and the French 4th Dragoon Division drove off the Russian cavalry.
Rather than the claimed "artillery charge", Senarmont's actions at Friedland were reactive and defensive. In putting the whole Corps artillery in a stop line, he probably saved DuPont's division from complete destruction. It was not particularly innovative or that well regarded - hence the lack of comment at the time. It became exaggerated by the post-war writing of Senarmont himself.