Technically, destroyers have AA stats as good as the likes of Tenryuu, and the AA specialists like Shigure have as good as anyone short of a battleship.
Historically, though, destroyers and light cruisers were the anti-air ships. Not because they carried more guns than the battleships, but because unlike KanColle's 6-slot-max, it was always cheaper and easier to carry a protective ring of destroyers and light cruisers than to pay the costs of more battleships. 12 destroyers with 1/6th the anti-air power each for less cost beats a single battleship, after all.
Historically speaking, all of the IJN warships were sub-par in the AA department in comparison to American and British ships. Inferior radar (or lack of them) and fire control systems, and no proximity fuses reduced their defensive capabilities against aircraft.
The Sanshiki incendiary shells were considered by American pilots as more of a pyrotechnics display than an effective AA weapon.
The venerable QF 2-pounder had a low rate of fire, short effective range and was too complex for the Japanese industries to mass produce it.
It's replacement, the Type 96 25mm did not fared much better: training and elevating was slow (even on power-operated mounts), the sights were inadequate against high speed targets, excessive muzzle flash and vibration made accurate fire difficult, the usage of fixed 15-rounds magazines lowered rate of fire (and the magazines had to be loaded by hand, since the Japanese never developed special tools for this task) and the 25mm rounds were too much light and short ranged to be effective against the fast and heavily armoured American planes.
The 12.7cm/50 Type 3 guns mounted on the majority of IJNs destroyers were of limited use against aircraft due their slow training (about 6 degrees per second) and rate of fire (the use of bagged charges instead of cased shells and the need to manually ram the shells required the guns to be re-aimed after every shot).
The 10cm/65 Type 98 gun was the best naval AA gun the IJN had at hand, but it's barrel had a short service life (thanks to the high muzzle velocity and fast rate of fire), and given the shortage of raw materials during the later stages of the war, the Japanese weren't able to build enough of them.
Although the Japanese captured a 40mm Bofors gun from British forces on Singapore, they weren't sucessful in reverse engineering it, due it's complexity.
Anti aircraft firepuka pukaAnd today is watermelon dayIt's vexing, but we destroyers are very weak and have no means to fight against aerial attack.July 27th
