I was going to reply to the other thread, but decided this was more generally useful given how many misconceptions there are about these weapon prefixes. It's also much easier to search for the answer to this question if it's in its own thread.

Before I explain, let me note that armor penetration (AP) provides a constant damage increase based on the AP percentage regardless of the DR of the target and your current armor penetration. This means that Anti Armor is just as good on the SBQ as it is on some random Ghoul (assuming you don't hit max damage coefficient). The formula for damage calculations is the same between FO4 and FO76, seen

here, and I'll prove this below.

Note that the base damage of the weapon is unmodified with AA, so these percents are true for both the damage coefficient calculation I show and the final damage numbers multiplied through.

Assume a 100 damage ballistic shot and a target base DR of 300

• Unreduced: `((100/300) ^ 0.366)*0.5 = 0.33445956848`
• Reduced: `((100/150) ^ 0.366)*0.5 = 0.43104300678`
• Damage Compare: `(0.43104300678/0.33445956848)*100 = 128.877%`
• Net Damage Increase: 28.877%

Assume a 300 damage ballistic shot and a target base DR of 300

• Unreduced: `((300/300) ^ 0.366)*0.5 = 0.5`
• Reduced: `((300/150) ^ 0.366)*0.5 = 0.64438731524`
• Damage Compare: `(0.64438731524/0.5)*100 = 128.877%`
• Net Damage Increase: 28.877%

Assume a 100 damage ballistic shot and a target base DR of 100

• Unreduced: `((100/100) ^ 0.366)*0.5 = 0.5`
• Reduced: `((100/50) ^ 0.366)*0.5 = 0.64438731524`
• Damage Compare: `(0.64438731524/0.5)*100 = 128.877%`
• Net Damage Increase: 28.877%

Assume a 300 damage ballistic shot and a target base DR of 100

• Unreduced: `((300/100) ^ 0.366)*0.5 = 0.74747450381`
• Reduced: `((300/50) ^ 0.366)*0.5 = 0.96332617745`
• Damage Compare: `(0.96332617745/0.74747450381)*100 = 128.877%`
• Net Damage Increase: 28.877%

That means that, like I claimed earlier, 50% armor penetration, such as from either rank 2 Incisor or the legendary prefix, always results in a net damage increase of 28.877% against everything in-game.

How Two Shot used to behave is that it would cause both bullets to deal 100% damage. That was insanely strong and easily beat AA at the time, but now it causes one bullet to deal 100% and one to deal 25%. This is important because if it actually caused both bullets to do 62.5% then Two Shot would be significantly worse than it is (seriously, do the math). Anyway, let's run the numbers, noting that we have to go through to the final damage since the base damage of each shot is modified.

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Assume a 100 damage ballistic shot and a target base DR of 300

• Unmodded: `100*((100/300) ^ 0.366)*0.5 = 33.4459568486`
• Two Shot: `100*((100/300) ^ 0.366)*0.5 + 25*((25/300) ^ 0.366)*0.5 = 38.4801477101`
• Damage Compare: `(38.4801477101/33.4459568486)*100 = 115.052%`
• Net Damage Increase: 15.052%

Assume a 300 damage ballistic shot and a target base DR of 300

• Unmodded: `300*((300/300) ^ 0.366)*0.5 = 150`
• Two Shot: `300*((300/300) ^ 0.366)*0.5 + 75*((75/300) ^ 0.366)*0.5 = 172.577575898`
• Damage Compare: `(172.577575898/150)*100 = 115.052%`
• Net Damage Increase: 15.052%

This shows that AA is actually significantly stronger than TS in all cases just from a pure damage perspective. We haven't even started talking about the nuanced behavior that TS weapons display with VATS and hip-fire (low accuracy / unreliable hit percentages in VATS). Note that this is also confirmed by anecdotal in-game testing such as here, though it's important to note that these are difficult in-game tests to perform because overkill damage is not factored into it at all (error of roughly 10-20% depending on specific tests taken). You might be able to do some more accurate in-game testing if you measured the pixel length of the remaining HP bar on enemies after each shot, which would be some cool data to have to back up the math.

tl;dr: Two Shot in its current form is actually significantly worse than AA in basically every possible way.

EDIT: Bonus damage gain table for various AP sources in-game to serve as a useful reference:

Source AP Effective Damage Gain
Perk: Incisor 75% ~66.1%
Legendary: Anti Armor 50% ~28.9%
Mod: Perforating Magazine 40% ~20.6%
Perk: Tank Killer 36% ~17.7%
Mod: Stinging Magazine 20% ~8.5%
Mod: Any Melee AP Mod 15% ~6.1%