AP/HE bombs comparison on T9+ BBs
I compared the damage between AP and HE bombs in the training room on T9+ BBs.
AP bombs
For AP bombs I flew 9 strikes on each of the T9+ BBs and then averaged the damage. Both squads were used to strike the same target together.
Montana - 21.493 damage per strike
Yamato - 19.795 damage per strike
GK - 21.640 damage per strike
Conq - 19.446 damage per strike
Iowa - 21.264 damage per strike
Izumo - 22.684 damage per strike
FdG - 47.119 damage per strike
Lion - 21.262 damage per strike
AP bomb damage is heavily dependent on damage saturation. The initial strike almost always caused damage in excess of 25k, reaching over 30k occasionally. Subsequent strikes usually deal around 15k to 20k. I once managed to saturate one Conqueror completely after three strikes at which point I only got 6k following up. This could be important due to heal, but on the other hand you will probably never fly against the same target more than two times anyway, so complete damage saturation should be incredibly hard to achieve and thus negligible.
FdG is the only T9+ BB vulnerable to citadel hits. You can probably sink her in a single strike in coordination with TBs. Or just straight up nuke her if you're lucky enough (though that didn't happen in testing).
(For a test on how damage saturation affects AP bombs, see a couple of posts below.)
HE bombs
For HE bombs I only flew 6 strikes per ship as damage was fairly consistent across the board, both damage saturation and nation of the target seemed to play no role whatsoever. Then again with fires being what they are I could never drop the same target too often so damage saturation may become a factor with heal in play, but as I said above it'll probably never be a decisive one since you're rarely ever going to attack a ship more than twice anyway.
Also I obviously ignored fire damage.
Montana - 23.353 damage per strike
Yamato - 25.179 damage per strike
GK - 24.437 damage per strike
Conq - 21.050 damage per strike
Iowa - 22.182 damage per strike
Izumo - 23.574 damage per strike
FdG - 21.919 damage per strike
Lion - 21.821 damage per strike
On a good drop you can expect anywhere between 20-30k damage, with opportunity to go higher. Bad drops yield around 10-20k.
Conclusion
As you can clearly see, HE bombs deal more alpha strike than AP bombs on T9+ BBs (although a very negligible amount). And can set fires. And break more AA. AND properly hurt DDs, too. In addition to that, AP bombs only deal high damage when the target is unsaturated, aka when you don't wanna attack it anyway because all AA is still operational.
So what are AP bombs good for? Well, I flew a couple of strikes against T10 cruisers for the lulz.
Hindenburg - around 15k damage per strike
Des Moines - oneshot without exceptions
Zao - either 35k+ damage or oneshot
Henry IV - oneshot without exceptions
Moskva - oneshot without exceptions
Minotaur - 15k+ damage, with the occasional oneshot
So yeah, if you wanna hurt BBabies, go for HE bombs. If you wanna celebrate "World of not Cruisers lol" and pray for cyclones or that people dont use DFAA, AP bombs will serve you better.
I would only truly recommend AP bombs for Lex as she has plenty of ships vulnerable to them in her MM spread. Even considering that I would not fault you for using HE bombs instead.
Follow up test: AP bombs and damage saturation
For this I specifically targeted different areas of a ship (in this case, a GK) to see if this method will yield more damage.
First target, first strike
Bow section - 27k damage
Aft section - 20k damage
Superstructure - 19k damage
First target, second strike
Bow section - 6k damage
Aft section - 13k damage + disabled turret Superstructure - 14k damage Second target, first strike Bow section - 25k damage Aft section - 25k damage Superstructure - 16k damage Second target, second strike Bow section - 15k damage Aft section - 13k damage Superstructure - 10k damage - sunk with 10 hits Conclusion This proves two things: 1. The higher damage yield from HE bombs comes from their larger drop circle, making them less affected by damage saturation as they hit more of the ship. Given enough strikes they should suffer from damage saturation just like AP bombs, but the amount of strikes required is more than two, thus thoroughly unrealistic to achieve as shown by the initial test. 2. You can emulate this behavior with AP bombs by specifically targeting the different sections of a ship if you cannot land citadel hits on it, which will result in higher initial alpha strike. The difference in damage however isn't high enough to justify using AP bombs over HE ones, as the ability to specifically target sections of a ship rapidly diminishes with the size of a ship (obviously) along with being potentially impractical in actual combat. HE bombs also still have the advantage in utility, being able to break more AA, set fires and doing good damage to DDs.
Aft section - 13k damage + disabled turret Superstructure - 14k damage Second target, first strike Bow section - 25k damage Aft section - 25k damage Superstructure - 16k damage Second target, second strike Bow section - 15k damage Aft section - 13k damage Superstructure - 10k damage - sunk with 10 hits Conclusion This proves two things: 1. The higher damage yield from HE bombs comes from their larger drop circle, making them less affected by damage saturation as they hit more of the ship. Given enough strikes they should suffer from damage saturation just like AP bombs, but the amount of strikes required is more than two, thus thoroughly unrealistic to achieve as shown by the initial test. 2. You can emulate this behavior with AP bombs by specifically targeting the different sections of a ship if you cannot land citadel hits on it, which will result in higher initial alpha strike. The difference in damage however isn't high enough to justify using AP bombs over HE ones, as the ability to specifically target sections of a ship rapidly diminishes with the size of a ship (obviously) along with being potentially impractical in actual combat. HE bombs also still have the advantage in utility, being able to break more AA, set fires and doing good damage to DDs.