Heavy ammo decreases the ranged armor of the target, making all subsequent ranged attacks against that target do more damage, but the reduction in armor doesn't apply for the initial attack that uses heavy ammo. The magnitude of heavy ammo is also pretty low, so it'll take several turns to really stack it up, and there aren't that many enemies that simultaneously have a high enough ranged defense for the stacking to be worthwhile, high enough HP to not already be dead by the time it stacks up, and are slow enough that there's time to stack it up before they get to you. Because of all this heavy ammo doesn't make that much of a difference in practice.

Precise shot applies the same kind of flat damage reduction to ranged defense, but applies instantly to each attack (but doesn't leave a lingering effect on the target). Both heavy ammo and precise shot differ from armor piercing shot because armor piercing is a percent reduction to enemy defense (50%), while heavy ammo and precise shot are a flat reduction. For enemies with lower ranged defense this flat damage reduction is better, but for the occasional enemy with a high ranged defense armor piercing can really shine. The best example of this is a scout/archer vs ghosts- even with a very high precise shot and high ranged damage the ranged attacks likely won't be able to overcome the ghost's ranged defense of 40, but give the scout a crossbow (armor piercing shot) and you'll suddenly start doing way more damage.

Overall precise shot tends to be the most useful, with armor piercing shot still being good for the few enemies with very high ranged defense, and heavy ammo only tends to make a difference towards the beginning of the game as a poor substitute for precise shot.

Heavy Ammo is more interesting on units like spearmen, who can apply several stacks of it with their thrown attacks before your scout unloads his bow into it. There aren't too many creatures where this is really necessary, although it can be helpful when you're first starting out and even a moderate amount of armor gives your scout grief.

Again, on beginner difficulty with heavy HP penalty to neutrals and bonus exp for your troops. Plus, early campaign have heavy penalty to AMOUNT of neutrals(for example, Heart of Labyrinth in early campaign have 2-3 minotaurs in guard, while default amount 12-14). There is no strategy on beginner :\
On higher difficulty levels even tier 3 cowtapult can't kill militiaman in one shot, and second ring can have 14 units in it.

Heavy ammo - stackable debuff to ranged defense.
Uses
1)Spearmen "prepare" target for finishing blow by Scout/another shooter.
2)Nice bonus on best arrows from castle shop (30 durability) with doubleshot.
3)Ballistae can get this bonus too, but their use is very-very limited. Somewhat effective for Siege engineers guard against inquisition raids(Executioner have 9+ Ranged def).

Precise shot - selfish ability to ignore some Ranged defense. This is really good on Sniper, with items he can stack so much Precise shot that only Ghost will have defense against him.