Today I try some real game test vs 400 AI naval bombers. The anti air heavy cruiser is dangerous, too easy to get sink.
So I switch to a BC anti air (not max tech yet). It get wounded 25%, and kill 40 naval bombers and have to go repair in 3 month. The 40 bombers cost is only equal to 1200 Military IC or 600 Naval IC, a MIL factory has output 2 times a Naval factory. So not worth to build it to kill planes, but is useful if you want to use the anti air BC as escort for CVs. Avoid naval bombers.
So I switch to a BC anti air (not max tech yet). It get wounded 25%, and kill 40 naval bombers and have to go repair in 3 month. The 40 bombers cost is only equal to 1200 Military IC or 600 Naval IC, a MIL factory has output 2 times a Naval factory. So not worth to build it to kill planes, but is useful if you want to use the anti air BC as escort for CVs. Avoid naval bombers.