An AD&D game is intended to span over a long career of players constantly facing new challenges. You cut your teeth on orcs and goblins, progress to bugbears, maybe ogres, then trolls, eventually you're facing bulettes and wyverns, then various species of giant, dragons, and by this point, you're world-beaters ready to hit the outer planes and tackle fiends and potentially demigods.
You will amass a great many magic items in this time, granting you powers and abilities beyond those of your character class, with only Wizards continuing to gain new powers until the high teens.
You might have crazy multiclass schemes, be dual classed Fighter/Wizards, have ability scores in the 20+ range, and possibly even wield artifacts.
At this level of play, the numbers are so inflated that combat becomes more about tactics and tricks than die rolls; a high level warrior isn't going to miss anything save for a roll of 1, and will be all but invulnerable due to super good saving throws, the lowest AC allowed, and various magical enhancements- your cloak of displacement will protect you from the first attack of the day, no matter what it is, your scarab of protection will let you save against effects that normally don't allow saving throws at all, and you have a double fistful of Ioun stones orbiting you at all times.
And unlike modern gaming, there are several good adventures for this tier of play, where you foil the schemes of demon princes and gods, and become legendary heroes...
Or maybe you died in a pool of your own blood at level 1 to a lucky goblin arrow. AD&D is a game of majestic mountains and seemingly endless chasms.
It's not easy to play. It's not easy to run, but it has it's own strange allure, like the sirens of myth.
As much as each edition since has promised to maintain that incredible endgame experience, something was lost in the translation. 3e shifted to being more about personal power, and most high level magic items are devoted to giving you immunities, big numbers, and mobility options- the real meat was in a plethora of strange abilities and feats which combined to create a sort of infernal Rube's Goldberg machine; when everything aligned just so, you were unstoppable. But often these builds proved delicate, and could be foiled rather trivially, much to the chagrin of their creators.
Organic development was shunted to the wayside; you now needed to plan out your character from levels 1-20, because deviation had a serious cost.
4e offered a taste of truly epic game play, but due to it's linear curve of development, combat felt mostly the same at every level- I love 4e, but it seemed like every new power was only a little stronger than the one it replaced, and the monsters had strange, bizarre abilities from the very earliest levels.
So by the time you get a Daily that lets you attack an enemy three times and leave them dazed until the end of the next turn, dazed (save ends) and stunned (save ends), enemies could have multiple hit point pools, transformations, and auras that prevented you from regaining hit points, along with immediate interrupts to teleport 10 squares away and stun you (save ends) for attempting to do anything so foolish as to attack them in melee.
With it's flattened math, feats, multiclassing, and magic items declared optional (and even beyond this, suggestion to limit magic items to a small amount), 5e characters may be fighting enemies with the same names as their nemeses of yore, but they won't feel anywhere near as powerful as those 20th-level AD&D heroes.
