I would say it entirely depends on if you plan to board or not. The AP-guns can't shoot grape, so, yeah, boarding isn't an option with them, unless you board with an ally, which leaves you to the whims of the AI.
But their special ammo completely ignores armour and inflicts very high damage, so there's no better weapon to sink ships other than going carronades.

Originally posted by Dat Scharger:

I would say it entirely depends on if you plan to board or not. The AP-guns can't shoot grape, so, yeah, boarding isn't an option with them, unless you board with an ally, which leaves you to the whims of the AI.
But their special ammo completely ignores armour and inflicts very high damage, so there's no better weapon to sink ships other than going carronades.

For some reason that just wasn't the case for me. I switched my entire fleet that was initially AP to Bronze Medium and sank all of them without a single ship being dismasted or getting below 75% hull health. When I had the exact same stuff other than that the last 2 times I had an ally ship captured in the first minute and my flag ship taken down to 20% sail durability
\_(.-.)_/

I'll try taking the ships on my next play-through to see if they have any buffs or not, so maybe the AP cannon will be slightly more useful there to try and kill more of the crew??

Edit: never mind the AP cannon doesn't have Anti-Personnel