AP certainly has more damage up front than AD. AD items are forced to be based around AD Assassin's and ADC's, where an ADC's job is to stay alive and deal consistent damage to an enemy team while staying alive to help siege, and an Assassin's job is to, well, assassinate a target quickly. There are a few niche items for champions (like Diana and Kayle) that can utilize a Nashor's Tooth well, however these champions are outliers and the items don't particularly synergize well with the vast majority of champions that deal damage in that sort of fashion.
Here's some AD synergizing items:
and
Damage does not stack. Statikk Shiv is build for champions like Vayne who lack waveclear or want wide-spread teamfighting damage. Rapidfire Cannon is built for champions like Caitlyn and Jhin to amplify their range and maximize siege potential (i.e. get that one juicy shot on a tower while maintaining safety outside range).
No longer gives Attack Speed on the active, only Movement Speed, and thus is more of a positioning tool for ADC's that build it (rarely now) or closing the gap for assassins like Zed. The Lethality/Flat Armor Pen nerfs to this item led ADC's avoiding this item that aren't an artillery-style setup (think Jhin or Varus).
Is an Assassin-based item, meant to amplify the "up-front" damage of a champion. It's beyond useless after being seen by an enemy champion (aside from a once every 90 second ward-sweeper). The bonus True damage is limited and often requires you to run Lethality runes to make up for the Lethality nerfs that have been suffered over the past few patches.
Is only efficient when rushed if combined with other Crit items, or on champions like Jhin (who is guaranteed a crit) or Gangplank (who heavily relies on the RNG barrels early-game).
Is similar to Infinity Edge. It does not provide a massive amount of stats without other items buffering where it falls short. It is usually rushed on champions like Ashe where CDR is their saving grace (i.e. walking Ultimate machines) or heavy mana-intensive champions that can utilize its passive well (Sivir, for example).
Deals 100 Flat Magic Damage now, and steals movement speed. The active portion was HEAVILY nerfed to be able to make it a more viable option for ADCs to bring into lane safely.
Scales off of BASE AD. While more AD will make your abilities hurt more, the only thing that will buff your Base AD is levels and
which sacrifices where you would likely build more damage/crit and instead opts for Health. The shield granted also scales off of your Health, making it harder to synergize well with full damage.
Scales off of BASE AD. The AoE zone is based on Armor, which again forces you to build defensive to utilize it more.
Gives 45% BONUS Armor Penetration. Key word here being bonus, it does not affect base stats, although most of the Armor you'll encounter is bonus, this is far inferior to Void Staff.
Gives a BUNCH of Health, +20% CDR, +40 Attack Damage, Shreds enemies for 5% armor on Physical Damage (stacks up to 6 times for a total of 30%) and grants 20 movement speed on hit, or 60 movement speed on kill (halved for ranged champions). This item requires you to be in combat and hit a champion a few times (aside from Ashe/Lucian who can stack it quickly with Q/R respectively).
+25 Attack Damage, +1000 Mana, Refunds 15% of Mana Spent, grants Bonus AD equal to 2% of total Mana, and a passive where single target attacks and spells (on Champions ONLY) consume 3% of currently mana to deal bonus physical damage equal to twice the amount spent. This item synergizes with basically itself, as there is not a large breadth of AD items that grant Mana. It also forces these champions to run themselves out of mana while fighting other champions, while dealing less and less damage while doing so. It's usually reserved for the likes of Jayce and Ezreal who can utilize its passive effectively in skirmishes.
Let's take a look at AP now:
Gives 100 Ability Power and 100 Free Magic Damage PLUS 10% of your ability power to up to 4 additional targets on hit (think splash damage). You're able to tag a minion or champion and execute a low health target, something that no AD champion (aside from perhaps Sivir or Miss Fortune, if enemies position poorly) has. So with 1000 Ability Power, Luden's Echo deals 100 + (1000 x 0.1) x 4 = 800 splash magic damage. It also gives +10% movement speed, something that is VERY difficult to match.
Gives 80 Ability Power, +10% CDR, +7% Movement Speed, +250 Mana, AND +75% Base Attack Damage (+50% Ability Power) on hit. This is the Trinity Force of AP Champions, giving that extra "oomph" where needed. The main difference is this item actually scales with stats. +50% Ability Power is nothing to scoff at, with 500 AP you're looking at +250 FREE Magic damage (not including Base AD, which brings it up even higher) on auto-attacks after using an ability, something that no AD Champion or item has a steroid that powerful to match.
Gives +40 AD, +80 AP, +15% Spell Vamp/Lifesteal (down to 5% for AoE), and an active that deals 175-250 (+30% AP) and slowing the target by 40% for 2 seconds. With 500 AP you're dealing (at minimum) 175 + (500 x 0.3) = 325 magic damage before resistances, and slowing the target by 40%. Think of this as the BotRK for casters.
Gives +120 Ability Power and +35% Ability Power. There is no AD item like this, aside from Infinity Edge with RNG. This is what makes Veigar become out of control with AP, and grants a gigantic amount of AP for literally ANY champion that buys this. It synergizes with every single AP item in the entire game, as well as Runes, Masteries, and bonuses granted from abilities/passives.
Gives 35% Magic Penetration. TOTAL Magic Penetration. It goes through base stats, unlike Last Whisper items.
Gives +15 Flat Magic Penetration, +300 Health, +80 Ability Power, and causes spells to burn targets for 2% Current Health per second (doubled to 4% Current Health per second against movement impaired units). This is a tank-shredding machine, and gives you a TON of survivability with the free Health.
+15 Flat Magic Penetration. This stacks with Liandry's Torment, and with proper Runes/Masteries allows you to hit champions that refuse to build MR (see greedy/poor ADCs) for nearly true damage. There is no Flat Armor Penetration boots.
Grants +60 Ability Power, +60 Magic Resistance, +10% CDR, and grants an aura causing nearby enemy champions to take +10% more magic damage. Great MR, more CDR, and an incredibly useful Aura for just existing. Black Cleaver may shred after hitting a target a bunch, but this item requires literally 0 effort for it to be effective.
Massive Health, Mana, Ability Power, and a super useful active AND passive. This item deals 100-200 (+35% Ability Power) Magic Damage to all enemies hit, as well as slowing them by 65%, decaying over 0.5 seconds. A very under-rated item.
Massive Health, +60 AP, +10% CDR, and one of the most useful actives in the game, giving a free dash to champions that have none and absolutely love that sort of stuff (think Evelynn or Annie). The active dashes forward and deals 75-150 (+25% AP) Magic Damage, and can strike the same target multiple times (deals 10% damage to enemies hit by multiple bolts).
+80 Ability Power, +1000 Mana, +3% of total mana converted to Ability Power, refunds 25% of Mana Spent, AND a free shield for 150 (+20% of current mana - consumed in the process). One of the most AP-efficient items in the entire game. For champions that already built a ton of Mana, this item simply gives them a massive pool of free stats.
+100 Ability Power, +400 Mana, +20% CDR, +20% MAXIMUM Mana Restored on Kills and assists, and FREE Grevious Wounds on targets below 35% Health? Yes, please! AD Champions must choose between dealing more damage with Lord Dominik's Regard or cutting healing with Mortal Reminder, AP champions have to make no such decision.
+40 Ability Power with an incredibly useful passive for cheap (1050g, the same cost as a Sheen) - 50-125 bonus magic damage on hit (40 second cooldown) on basic attacks. This item also builds into the other Hextech items, which contain some of the most useful passives in the game.
One of the best early-game items around. At level 1 this item grants an addition +30 Damage while granting +24 gold (if hitting with 3 spells) and continuously generating stacks over time to do it all over again. It also grants +2 gold per 10 seconds, +25% base mana regen, and 5 ability power. There are no AD items that can match this.
As you can see, AP items are far and away more capable of "murdering someone." Sure, a 100% Crit late game ADC will melt your entire team, however you will melt them with a FAR easier time due to sheer stats, hence why ADCs are targeted in teamfights and the whole "ADCin2k17LUL" meme came from. Hitting an ADC with an Ahri charm is a death sentence for them, where they will likely lose their life or be forced to retreat, whereas hitting an APC from a close range with an Ashe arrow is a stat-check for the ADC, and still allows the APC to turn and deal significant numbers, while also requiring the ADC to still dodge your abilities (slowing down their chase and worsening their chances of actually killing you without assistance). If you don't shut them down, their continual mana-free right-clicking will melt you eventually. This requires extreme mechanical interaction from the ADC to dodge all of your spells and CC, as well as being able to be in a position to keep damage up on you. A Draven doesn't run in and 3-shot you without you letting him pick up his axes and deserving it. A 1500 HP ADC stands no chance against a 3000 HP Ryze running at them with point-and-click and requires mechanical failure of the AP to succeed.