This is a comparison of the Union 12-lber Napolean and 20-lber Parrot artillery guns.
Both do 2 hit points of damage upon an actual hit.
In addition to this, the Parrot does 22 points of cohesion loss and the Napolean 12.
The to-hit chance is a long equation that is the same for both guns save for their respective Offensive/Defensive factors. The Parrot's numbers are 23 Off./24 Def. and the Napolean's are 16 Off/30 Def. So the Parrot will cause 7% more hits in the attack than the Napolean and the Napolean will cause 6% more hits in the defense than the Parrot.
The Parrot has a range of 7 and the Napolean has a range of 5. However, most terrain/weather combinations allow an effective range of 4 or less.
For the initial analysis, I will compare the two guns in an attack with 15 batteries of each against a force entrenched to level 4 in a region with open terrain and clear weather, so max effective range for both guns.
The 15 Parrot batteries fire twice at range 7 and then once at each successive range for a total of 120 shots fired. Let's be generous and say that half the rounds hit, for 60 hits scored. Level 4 entrenchments negate a third of these for a new total of 40 actual hits. The defending force loses a total of 80 hits and 880 points from cohesion.
The 15 Napolean batteries fire twice at range 5 and then once at each successive range for a total of 90 shots fired. The Parrots get a 7% bonus to-hit, so that would only give a 43% to hit rate for the Napoleans for a total of approximately 38 hits scored. Again the level 4 entrenchments negate a third of these for a new total of about 25 actual hits. The defending force loses 50 hits and 400 points from cohesion.
However, conditions are seldom perfect. If the CSA is wise enough to make a stand in a woods region with effective range of 4, then the Parrot's numbers are 75 shots fired, 38 hits scored, 25 actual hits for a total loss of 50 hits and 600 to cohesion.
The Napolean's numbers are 75 shots fired, 32 hits scored, 21 actual hits for a total loss of 42 hits and 336 to cohesion.
So for a Union player on the attack who doesn't mind the pricetag, the Parrot still gets a cracker.

I'm the 51st shade of gray. Eat, pray, Charge!