AD champions are not significantly stronger than AP champions.

Magic carries are simply less common than Physical carries.

Physical Carries

Physical Semi-carries

Magic Carries

Magic Semi-carries

AP champions, as a general rule, fall flat in terms of raw carry potential. They have flaws in their kits that simply make playing them as a carry a mute point. Some have poor persistent damage (Lux). Some have high persistent damage, but it comes out over a long enough period that they can't kill reliably late game (Malzahar). Some have high persistent damage, and it comes out at a good rate, but they don't have the burst to finish people off (Fiddlesticks). Some have both burst and DPS, but are just completely unreliable (Heimerdinger).

The League community seems to equate "Carry" to "Anyone who does a lot of damage", and that simply isn't true.

The role of an carry is to a major force that drives the end of a teamfight in your teams favor, and to take objectives after the fight. If one side has a living carry and the other doesn't, the side with no carry will take a very long time to kill the enemy front line, allowing the enemy carry to break through their front line and start shooting the back line first.

The role of a semicarry is varied. Some are there to deal ambient damage to everyone (Fiddlesticks). This makes it easier for the carry to wipe out the enemy, but also means that it will be easier for one of you to clean up if the carry dies. Some are there to deal heavy burst to a single target (Zed). This dramatically swings the fight in your favor by getting rid of a major enemy disruptive force (whether that be a carry dealing damage or a Soraka undoing damage), but you don't typically contribute a whole lot else to the fight. Some are there to provide utility and disruption alongside their damage (Lissandra). These guys are essentially supports on crack, setting up their teams for success through means other than damage, while not lacking damage themselves.

Oh, did just pop off and kill your entire team, while your poor never could have done the same? No, that doesn't mean "AP is under powered". is not a carry. can't do that, but you can bet your ass can.