Using Armor
Tanks
You have three choices of tank here: heavy, medium, and light.
Predictably enough, the heavier a tank is, the more damage it will be
able to take and dish out, but the slower and more expensive it will
be. This can make for some interesting dilemmas, depending on what kind
of player you are. If you like to advance forward and capture control
points, you may want to use a mixture of medium and light tanks, as
you'll be able to make a lot of units and spread them out among the
perimeter points that you'll be assaulting. If you're going to be
hanging back and defending, then heavy tanks will prevent any enemy
armor from getting too close to your perimeter points, especially if
you manage to find the high ground.
You also can't lose track of the special abilities that each tank has. Offensively speaking, the special abilities of the heavy tank let it quickly killed light tanks and armored carriers, the medium tank will be best used against infantry, while the light tank will be able to deal more damage to heavy armor with its special ability than it will with its main cannon. All of these tanks can pop smoke screens, which will shield them from view for ten or fifteen seconds; pretty handy when choppers come a-callin'.
APCs
Bringing up the rear are the armored personnel carriers, of which there are regular and amphibious variants. These are mainly intended to shephard infantry units to the front lines, so if you see a friendly player's infantry slogging their way across the battlefield, try to give some of them a ride. APCs are very lightly armed, but their machineguns can take out enemy infantry relatively well and also fire on enemy choppers, although this will most likely just wind up in them getting pasted by missiles. It's probably best to simply spend your points on actual tanks here, but if you team up with someone playing infantry, you can definitely get some mileage out of APCs.
Defeating Armor
Heavy choppers are the undisputed kings of tank-killing; one or two heavy choppers will be able to destroy almost any tank with a single full barrage of their missiles. Their Hellfire missiles will also be devastating to tanks. If a squad of your tanks comes under fire from choppers, quickly pop some smoke shields off and call for help, or simply call down an air-to-air strike on your adversaries. Just remember that if you have a large number of tanks in a single squad that all of their smokescreens will go off at once if you use the R button shortcut. You might want to cycle through your tanks individually and pop off their smoke screens one or two at a time to ensure that your tanks survive until help comes. Tanks can't do much to attack choppers directly, so if you get caught out in the open you're probably toast unless someone helps you out.
Anti-tank soldiers are next up in the queue. Their rapid-fire anti-tank weaponry will quickly destroy light and medium tanks and will eventually take out heavy tanks, given a couple of reload periods. If you run headfirst into anti-tank soldiers, you can quickly pop smoke and then use the SHIFT+N shortcut to tell your tanks to back away from the enemies, if you don't mind retreating; it's better than dying. Alternately, if your enemies are out in the open, you can charge into them by clicking on the ground past them; you'll probably pound a few of them underneath your treads. Tanks, again, can't do much offensively against infantry, since their machineguns don't really work too well on them. Medium tanks can use offensive abilities on them to destroy them, however, and APCs will be able to slowly machinegun them down.
Artillery is also adept at quickly taking out tanks, but will need to have some help spotting them. That said, there's no greater thrill than ruining an enemy's very expensive heavy tanks from halfway across the map. Fighting back against artillery requires more than a smokescreen; those might as well be big target markers for artillery units. You'll need to get help or use tactical aid to destroy them.
In terms of tactical aid, strong dedicated strikes like tank busters and heavy air support are best at taking out enemy tanks. If you're going up against light and medium tanks, then heavy artillery barrages can usually wipe them out, but heavy tanks will generally escape without being destroyed unless you layer multiple strikes on them.