1940 AA in particular is a pretty big jump up for AA strength, and RADAR buffs that massively from 1940 onwards. It tends to be a good idea to go for both since they have some dual-purpose utility (1940 and later AA is great for nations without air superiority). Its pretty doable to get up to 20 AA per cruiser* or battleship based on mixing DP secondaries with 1940+ radar and 1940+ AA.
*Cruisers need more equipment/tech to hit 20+, but 2 AA modules and FC can bump them up; with 3 DP secondaries and 1940 AA/radar, its closer to 12 AA)
For destroyers, however, its usually too expensive to practically get any meaningful AA rating on them without a significant cost increase for them. I'd rather build destroyers with little or no AA, and focus on max-AA cruisers and battleships (capital ships benefit individually as they tend to be the ones getting bombed, while cruisers can benefit from the stacking AA % bonuses while relying on relatively-affordable DP secondaries). The problem with arming destroyers with DP primaries is both the higher cost, but also the +1 steel for mounting them. By comparison, AA and DP secondaries don't cost steel, and can be refitted on older ships more affordably.
For some perspective, a minimalistic destroyer costs around 1100 IC with Gun-2, Torpedo-2, Depth Charge-2, and engine-2. The cost climbs to 1500+ if you try to mount DP guns, AA-3, and an extra module (whatever you want in the 3rd mounting, whether more torpedoes, depth charges, AA, guns). Its reasonable as the US given your massive steel stockpiles and the fact that you are going to be operating against a lot of enemy aircraft (the Axis really can't go head-to-head vs the Allies without naval superiority), but that's about it. Britain, Germany, and Japan really lack the steel and NIC to produce high-cost destroyers for good AA ratings without compromising on other things like cruisers (or steel-expensive ground equipment like tanks or 1942 rifles). A high-AA destroyer is also still only going to be likely 10+ on AA for that cost.