You don't use an A/A anywhere in the system, you have a second 'radiator' dedicated only to the air/water system, which chills the coolant water - this water is then pumped through a smaller radiator, enclosed in a shroud, installed in the engine bay. The hot intake charge is passed through this engine-bay mounted chilled water radiator, cooling the intake charge. The main benefit of A/W is reduction of heat soak; you're pumping the coolant away from the hot engine bay, to a remote location where it can be efficiently cooled; in addition, you're able to maximize placement of the cooling components without the restriction of trying to keep the charge pipes as short as possible; you can stick the cooler in the front of a mid engine car, then just pump the water into an in-line intake charge heat exchanger, such as a bullet unit from lama nova.
Essentially, you reduce design considerations, and can create a system which is capable of more efficient cooling; it's a better system, unless you have a situation where an A/A setup can be simple and efficient, such as on a porsche with a turbo tail, or a front engined car such as a supra. On a mid-engined car, it's very difficult to find a suitable air/air intercooler placement that won't be affected by heatsoak.