Okay, so I programmed it into Excel. Armor band 19 cells wide (15 cells hittable). I set it for 1500 base armor, 14000 hull, taking fire from a weapon that does 500 HE damage per shot.

Assuming uniform distribution, it kills the target in 46 shots; after the 46th shot it'll have done 8850 damage to armor (out of 9100 total armor in cells) and 14197 damage to hull.

I tried 3 normal distributions:

1. mean = 0, stdev = 1, x = {-1.05, -0.9, ..., 0.9, 1.05}, and then normalizing. This represents the center 70.6% of the distribution, i.e. 29.4% miss. The chance of a shot hitting the center cell is 8.1%, while the chance of a shot hitting the cell at the end is 4.7%, so hitting the center is about twice as likely as hitting the end. Then it kills the target in 46 shots; after the 46th shot it'll have done 8589 damage to armor and 14360 damage to hull.

2. mean = 0, stdev = 1, x = {-1.4, -1.2,..., 1.2, 1.4}, and then normalizing. This represents the center 83.8% of the distribution, i.e. 16.2% of the shots miss. The chance of a shot hitting the center cell is 9.2%, while the chance of a shot hitting the cell at the end is 3.5%, so hitting the center is about 3 times as likely as hitting the end. Then it kills the target in 45 shots; after the 45th shot it'll have done 8456 damage to armor and 14227 damage to hull.

3. mean = 0, stdev = 1, x = {-7/3, -6/3,..., 6/3, 7/3}, and then normalizing. This represents the center 98% of the distribution, i.e. 2% of the shots miss. The chance of a shot hitting the center cell is 13.5%, while the chance of a shot hitting the cell at the end is 0.9%, so hitting the center is about 15 times as likely as hitting the end. Then it kills the target in 43 shots; after the 43rd shot it'll have done 7112 damage to armor and 14061 damage to hull.

Basically as the variance decreases and the shots get more accurate, it's more likely that the shots will land on a spot where the armor's already cleared out, and thus less damage gets done to armor and more damage gets done to hull, so the target dies a bit faster, even when counting by number of shots that actually hit. (Uniform distribution is effectively a normal distribution with infinite variance that's then normalized.) The difference is relatively minor though.

Now if we assume the shots hit one at a time, rather than a probability wave. Uniform distribution across 15 hittable cells. For 200 samples, the average damage to armor after 46 shots was 8684 +- 270, and the average damage to hull was 13727 +- 213. So modeling it as a probability wave rather than simulating individual shots one after another meant it overestimates damage to hull by around 3.4%. So, fairly close.

So realistically the models are going to be within say around 10% of each other whether you look at it as uniform or normal distribution, and whether you simulate it as a probability wave hitting all at once or as discrete shots hitting one after another.

Edit:

In both of these cases, you've adjusted the variance of one of the distributions to match some statistic of the shifted mean distribution (either hit% or TTK), but you end up with a totally different situation overall that isn't really a useful comparison. If you don't care about this distinction, there is no point in simulating the armor cells at all.

It's not that adjusting the mean vs the variance will always mathematically have the same effect when fitting model to data. It's that for the purposes of the model simulating combat, this edge case of "super accurate weapon that's always nicking the very side of the hittable part of the ship" is not something worth considering. I don't think it's worth planning a weapons loadout around barely hitting one side or another of a ship.