AD&D characters have 3 armor classes. Armor class of base armor, armor class with dexterity bonus, and armor class with shield and dexterity bonus. Different types of attacks hit different armor classes. Frontal attacks strike against the maximum AC provided by worn armor, shield and dexterity bonus. Flank attacks negate the shield. Rear attacks negate the shield and dexterity bonus. Only the official AD&D sheets have separate entries for the different armor types, all the online player created sheets I've seen ignore this completely.
The weapon vs armor tables are used against worn armor and shields only. This is due to an obfuscation of the Man-to-Man combat table from Chainmail, which explicitly gave certain weapons bonuses against certain armors. A shield's bonus is only applicable to armor class depending on its size. Small shields only provide a bonus against 1 attack a round, Large shields provide a bonus against 3 attacks per round.
The only reason to use the weapon vs. armor charts is to limit the power of swords. The base stats of swords do more damage and have more favorable reach and speed factors than all other weapons. However, swords only get a "to hit" bonus against the lightest types of armor, and do poorly against heavy armors (except the two handed sword). There are less than a handful of weapons that can harm the heavy armors - maces, morning stars, the heavy cavalry lance, flails, picks and halberds. Basically, clerics and paladins present the greatest danger to heavily armored foes.
The weapon vs armor table basically makes armors that were hard to hit, even harder to hit and armors that are easy to hit, even easier. Most monsters in AD&D do not carry the weapons required to hit heavily armored characters, so in order to provide a challenge the DM has to specifically equip monsters with the higher bonus providing weapons.
The Sword, Two-Handed is far and away the best weapon in any consideration. It has a bonus to hit every class and does the most damage of any weapon. It has a favorable length and space required to swing. It's only drawbacks are its high weapon speed factor, which means it will lose initiative against ties, and in the case of a tie the opponent may make multiple attacks against the two-hander, and it will basically be unable to interrupt a magic user from casting a spell. In my games, I allow players to walk through 10' corridors at a formation of 3 characters abreast, but restrict them to using only weapons that have less than 3' space required. The "standard" D&D grid uses 5' squares, and most player characters choose to march two abreast down a corridor. The two handed sword requires 6' space to use, so I'm going to have to come down hard on that requirement to restrict players from using a two-handed sword in situations where they would hit an ally.
Most polearms have long reaches and have small space required to use. This makes them really advantageous in tight formations and to fight over the space of another character. Attacking from the second rank is the greatest advantage of polearms and is the justification for their use. Once the polearm bearer is engaged directly, he should abandon his polearm for a more favorable personal weapon.
Frank Mentzer considers AD&D to be more of a wargame than the looser, more open OD&D strain. I agree, and prefer to lean heavier on the wargame aspects of AD&D than the magic. I try to treat the dungeon as a long field expedition.
All this was prompted by a game of AD&D in B2 The Keep on the Borderlands, in which I had two Paladin player characters, who started with average armor and then quickly bought plate armor and shields and became nigh invincible to monster attacks and weapon damage. The only way to harm those characters was to equip monsters specifically designed to harm them, and to play them to the hilt using ambush and flanking tactics. It really drove home to me that the real difference between AD&D and any other strain of D&D is the combat aspect of it, and if you're not using all of AD&D's combat rules then you might as well play any other edition.
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