As their name implies, Anti-Airs are strong at fighting Air units, but are also strong at combating foot soldiers and light vehicles.
The primary use of an Anti-Air is to fight Air units. Anti-Air do very high damage to them, especially Copter units. Anti-Airs have little to fear from B-Copters in particular, taking minimal damage from them while dealing extreme damage in return. Anti-Air also deal high damage to plane-type air units, while costing significantly less in the process.
Anti-Airs are also capable of decimating Infantry and Mech units, with a full-HP Anti-Air capable of instantly destroying them if they are on Roads. With any form of attack boost, this result will also be guaranteed on Plains, and has a moderate chance of happening on Forests. This can prove invaluable in punching through a defensive line of Infantry that Tanks could not otherwise handle on their own. Anti-Airs are also decently effective at attacking light-armored units, such as Indirects, but less powerful than Tanks in this regard. Anti-Airs deal poor damage to Tanks, and next to no damage to any heavier tanks, so those units should be avoided.
Despite their increased defense against Air Units and higher cost than Tanks, Anti-Airs have worse armor than Tanks in terms of Ground combat. Tanks, Mechs, and Indirect Units will all do significant damage to an Anti-Air, so care must be taken around these units.
The most direct counter to an Anti-Air is a Tank. Tanks will beat them handily in Direct Combat, dealing much more damage to Anti-Airs than they will take from them. Mechs will also deal significant damage to an Anti-Air, but only if it can get the first strike. Otherwise, the Mech will likely be destroyed or severely crippled. Likewise, Bombers will heavily damage Anti-Airs if they can get the first strike, which is fairly easy given the Bomber's increased movement range and ability to fly over terrain. Again, getting the first strike is critical, as Bombers will take heavy damage from Anti-Air otherwise. Anti-Airs are also incapable of attacking a hidden Stealth, so they can attack Anti-Airs with impunity.
Since Anti-Airs are a hard counter to B-Copters, one should never engage in such a battle with a B-Copter unless the Anti-Air has 3 HP or less. Damaged Anti-Airs can still do significant damage to B-Copters otherwise. It is generally preferable to avoid the Anti-Air's line of fire with B-Copters. This can be done fairly easily, despite their similar move ranges, thanks to the fact that B-Copters are not hindered by terrain features. Use forests and mountains to your advantage to move B-Copters in positions that allow it to attack but make it difficult or impossible for an Anti-Air to retaliate against.
When an enemy fields Anti-Airs, care must be taken with any defensive formations with Infantry at the front. Anti-Airs are highly likely to outright destroy even full-HP infantry, leaving shielded units vulnerable to follow up attacks. When shielding with Infantry, it is advisable to use more defensive terrain to your advantage, and possibly having a second layer of Infantry to protect vulnerable units in case the first line falls. At the very least, a good course of action to take is to ensure that any lines broken by enemy Anti-Airs will be more costly for them than it is for you.