Italy as per Japan had not done much in the way of ASW / AA / or radar
development and the price for the Axis merchant shipping was high.
Italy was more restricted.
Italy had around 25% the steel production that Japan had.
Italy was learning and did improve things somewhat although slowly.
For ASW the Italians were helped by the clearer water and calmer seas (less wave action) but that was not a real solution.
The Italians had some mediocre AA guns but not enough of the them, production may have been a problem?
The Italian 37mm
was sort of a low grade 40mm Bofors.
Which put it ahead of anything that the Japanese had under 75mm in size.
It was also better than the British pom pom on per barrel basis, but we are comparing twins to quads or octuple and that gets harder.
German early Navy 37mm AA guns are pure crap. They don't get better until 1942 or later.
Italian basic problem is there aren't enough of the them. Most of the Cruisers wound up with 4 twin mounts which for 1940-41 wasn't really that bad. They didn't get more which was bad.
Most Italian destroyers were no worse off than the British WW I and the A-I Destroyers at built. Either licensed WW I 40mm Pom Pom (two per ship) or a smattering of 13mm machine guns. Higher powered but slower firing than the British .5in guns.
Different gun action but remarkably similar in performance to the Japanese Navy 13mm AA guns. With just 2 twins per ship as built they weren't any worse than many of the Japanese destroyers as built.
Both navies swapped the 13mm guns for heaver weapons. the Japanese went for the infamous 25mm while the Italians went for the 20mm Breda gun.
The Breda used the same ammo as the German 20mm Flak 30/38 and fired about as fast the Flak 30 ( much slow than the Oerlikon).
Main practical difference was that the German guns used 20 round magazines that had to be changed and the Italian guns used a 12 round tray that feed through the gun and dropped out the other side (?) making reloading a bit easier even needing a bit quicker.
Italians often swapped a twin 20mm for a twin 13mm so the increase was a bit marginal but the Germans and British weren't doing much better in 1940-41.
Japanese waited until 1942 to upgrade many of their destroyer AA guns. Made US water cooled, belt feed .50cals look like wonder weapons
Italian twin 20mm mount.
One gunner and 4 loaders (?)s
It might have equaled a single Oerlikon gun for fire power and in 1940-41-early 42 there were not a British destroyers running around with more than 2-4 Oerlikons.
Italians may not have had the directors/fire control on the main guns that the British had on their destroyers but with the low elevation of the main guns in either navy their success was in breaking up attacks/causing planes to drop early rather than shooting anything down.
British got better in 1943 and later but we do have to be careful as to the years.