Points of Light
The 4E Dungeon Master's Guide defines the parameters of a typical D&D campaign in the setting section. The default setting is called Points of Light, which describes how the world is mostly wilderness, full of monsters and ancient ruins, and peppered with occasional safe havens (typically villages and small cities).
Exception Based
The 4E game is exception based. Where AD&D defines rules for this and rules for that and a different class might have its own system (e.g., thieves), the core 4E rules are very simple. On top of that very simple core, add exception after exception. If you've played Magic: The Gathering, you've seen this principle in action.
To great effect, 4E defines classes primarily with powers. Every class works pretty similarly in this regard. The difference is in the list of combat powers that defines each class. Each power provides an exception to one or more rules, to be used in specific combat situations.
Skills
Most versions of D&D have some idea of non-combat skills that any character can learn. In AD&D 1st Edition, it's the "secondary skills" table in the DMG. In 2nd Edition, it's non-weapon proficiencies. 3E and 4E add a true skill system. The game calls for you to roll these skills all the time. 4E adds a skill challenge system for handling non-combat obstacles that require effort over an extended duration.
I and many other people love the idea of skill challenges but hate the 4E implementation. Find Stalker0's Obsidian Skill Challenge system and use it instead. It's fantastic and solves all my problems with the built-in system.
To Level 30, Tiers
AD&D didn't have level limits, but it got pretty unwieldy after a certain point (some say 6th level). By unwieldy, I mean that the DM's effort to create encounters just gets harder and harder as the characters level up. 4E makes encounter building a lot easier.
4E also takes the characters to level 30 with clear sets of powers for each level. It does this in three, 10-level tiers: heroic (1-10), paragon (11-20), and epic (21-30). Play changes a bit at each tier, and the kinds of encounters PCs face (and where they adventure) changes considerably.
Dynamic Combat
AD&D combats mostly turn into characters in fixed positions trading blows with monsters until one side loses. There's not a lot else going on. In 4E, the standard/move/minor action system gives players a lot of options every turn. A typical round for a rogue includes moving around (avoiding opportunity attacks by shifting), attacking, and maybe some kind of minor action to boot. A lot happens in six seconds! (Oh yeah, combat rounds are six seconds, not a minute.)
Gonzo
4E is way more gonzo. Or laser-sharked. Whatever term you use to describe it, 4E has lots of weird races and classes as PC options. Play a goliath ardent, a dragonborn sorcerer, a tiefling warden, etc. The old races and classes are still there; don't worry. Just expect spikes and horns on everything (not really, but it sure feels that way).
Power Sources
4E introduced the idea of distinct power sources to the game. AD&D differentiated between types of magic, and dumped illusionist magic in with magic-user magic but separated them from clerical divine magic. 4E gets explicit about where a character's power comes from, even if he's a fighter. You have the martial power source for fighters and rogues, the arcane power source for the magic-user types, divine magic for the clerics and other religious types, primal power for druids and the like, and the psionic power source for a host of mentally-driven characters.
Defenses, Saves, Death
All different! Be careful here.
You have four defenses: Armor Class, Reflex, Fortitude, and Will. Basically they took effects that used to require a saving throw to avoid and turned it around. Now you have a defense against those things. The fireball attacks your Reflex. The illusion attacks your Will. You don't have to roll anything to avoid it. They either hit or not.
And while we're talking about AC, gone are AC to-hit charts and THAC0. You roll d20 + bonuses and try to meet or exceed the defense (AC or otherwise) to hit. Simple enough.
Saves still exist, but they're for shaking off lasting effects. Say you're taking ongoing damage from being on fire. At the end of your turn, you get to try to save against the effect. All saves are the same: roll d20 and get a 10 or higher. Simple as pie. Mmmm, pie.
If you fall under 0 hit points, you're unconscious and dying. Every turn in combat, make a saving throw. 10+ and you don't get worse; 1-9, and you get one strike. Three strikes, and you're dead. Roll a 20, and you get to use a healing surge! Oh, the negative-10-and-you're-dead thing changed. Now you get to go negative equal to your "bloodied" value, which is half your maximum hit point total. Pretty sweet.
Toughness
In general, 1st level characters are pretty damned tough. However, the monsters they face are pretty tough, too. Your 1st level rogue might have 23 hit points, but the kobolds have 27. (Just making up numbers, but you get the idea.)
Encounter Scale
Encounters in AD&D (and really every version before 4E) were pretty much focused on one small area, typically a single room. You go into the 10x20 room and fight monsters. 4E encounters sprawl over multiple rooms because of all the extra movement. It really feels like a big fight, dragging in monsters who overhear the noise. Or you might loop around the back way to flank the boss.
I played many years of 2e (and BECMI, 1e. 3e. 3.5e, PF, and OSR stuff) and have read the 5e PHB, Basic set, and Hoard of the Dragon Queen and played some short games, so I think I can give some good points of comparison. I'm excluding the Skills & Powers stuff in late 2e from this discussion, that was less like 2e than many other versions of D&D itself.
There are definitely similarities between 2e and 5e — mostly conceptual and "feel" similarities. The individual mechanics are different — pretty much entirely, except for the basic "rolling to hit involves a d20! AC is involved! And there's saving throws of some sort!" kind of things all the editions share; none of the numbers or tables or rolls are identical.
It's almost as if 5e was a do-over of 3e, with the benefit of many hard lessons learned from the 3e → 3.5e → 4e experience, mostly about limiting power inflation but avoiding the risks of trying to mitigate that through making everyone the same. I think it's fair to say that in retrospect 3.5e is a min-maxer's wet dream and dissolves into non-fun at moderately high levels from rocket tag and op disparity; 4e tried to fix that but was in the end unsuccessful because it made everyone vanilla and identical in the process — reminiscent of in WoW, how "At level 1, you kill boars... Now that you're level 70, you can go farm level 70 demon boars!" (See also: Some Thoughts On 2e and 3e's Legacy.)
Power Limiting Through Mechanics
5e uses bounded accuracy and advantage to obtain the same power differential limiting that 2e did with just "fewer bonuses." Everyone's addicted to bonuses now, so you can't not have them, but they take a different tack to try and get a power level more like 2e's. In 2e, for those who aren't grognards, there was a lot less difference in power with level and/or Hit Die. You just couldn't stack many bonuses on top because they weren't available. A level 5 person wasn't infinitely more than level 1 or less than level 10, the curve was less steep. 3.5e easily degenerated into people with +0 bonuses and +30 bonuses and "rocket tag." The 5e mechanics are trying to solve that problem with a different mechanical approach, but with a result that feels like halfway between 2e and 3e power level wise.
You'll hear people with yesteryear's goggles on complain about "all those unbalanced kits in 2e!" If you actually go back and read the kits after playing 3.x+, you'll wonder what the big deal is. Most kits would at most get you a free weapon or nonweapon proficiency. One of the most "unbalanced," the Berserker, lets you get a +1 to hit/+3 to damage by going berserk (raging). An 18 STR gets you all of a +1 to hit/+2 to damage in 2e. Back in the day, combining that into +2/+5 was a HUGE bonus — now, we call that "a first level character's standard attack and damage bonus, if they are poorly optimized."
The 5e class configurability options are like a cross between 2e kits and Paizo's class archetypes — more like the archetypes in how much of the character they swap out, but more like kits in terms of "choose just one, permanently."
Power Limiting Through Randomness
Rolling stats reduced power by reducing optimization. That was stock in 1e/2e and is back in as the default gen method in 5e (things went all point buy in the interim).
The concept of creating and buying "to spec" magic items introduced in 3e has also been removed. It was a lot harder to come up with broken combinations when you couldn't just "sell that thing I just found for 50,000 gp and demand the perfect 50,000 gp item for my build in return." In 3.5e you had a "wealth tax" in that you were expected to have a whole suite of +(level/3) enhancements to everything.
So it feels like 2e, more than it feels like 3e/4e, because you can't custom craft every aspect but have to rely on the campaign and luck to a degree.
Other 2e-Like Stuff
The one thing that really struck me was the art similarity between the 2e PHB and the 5e PHB on the interior art. Especially the full-page color plate pics but also the character treatments really made me think "2e!" while I was reading it. Each edition has had very specific art direction and 5e's looks a lot more like 2e's than any other version.
The skill mechanic has been dialed back from "lots of skills" to more like the 2e NWP mechanic where really you just have a couple, while retaining the 3e style mechanics.
Spells and stuff are just shorter, too. This makes it feel like 2e just because it was a midpoint between the more terse BECMI and the more verbose 3e. (e.g. Knock spell — BECMI: 122 words, 3.5e: 206 words, 5e Basic: 132 words)
And finally — attitude. Mike Mearls and the WotC team have been trying to get everyone to take responsibility for their own game and rules again. The GM guidance in 5e is conceptually similar to the strain in BECMI and 2e per How has D&D's guidance to DMs on when to extrapolate from written rules and when to improvise changed over time? A lot of the confusion over his talk about "living rules" is a straight up conceptual shift - he talks about "living rules," and then people only familiar with 3.5e and/or 4e turn it into "Living Rules(tm)" and debate its exact definition. He's just saying "Goddamnit people loosen up!" In 2e we house-ruled a lot; any 3.5e/4e question about house ruling here is usually answered with a Careful Admonition To Not Do So Lest Ye Upset The Holy Game Balance. They're basically trying to bring some of that old approach back — I guess we'll see if they can change their fanbase as easily as in the past or if that's a Pandora's Box that it's hard to close.
A Bunch Of Non-2e Stuff In 5e
Of course 5e also has a bunch of stuff from 3e — feats, similar core mechanic (THAC0 replaced with the pure d20+bonus vs difficulty), similar way of stating rules, multiclassing, no level limits.
It also has a couple things from 4e — mainly weird proud nails from the "UberBalance" (like the "you have to use your action to make your animal companion attack!" bit). And healing surges transformed into Hit Dice recovery made confusing by sticking the "Hit Dice" term on it. Monsters being not like characters is 4e-ish but also 1e/2e-ish.
It has very little from 1e that wasn't also in 2e; the focus on the "three pillars" of combat/exploration/interaction for example, is familiar from 1e but also in 2e. 1e and 2e were mainly different in that 2e cleaned up the super arcane parts of the rules (to-hit tables) but also cut the super arcane parts of the fluff (most of the DMG, including random harlot tables).
And 5e has some net new stuff not from any previous editions, like the indie-game inspiration and bonds and stuff.
Railroading
I actually like most of the stuff that 5e has in common with 2e. However, after reading Hoard of the Dragon Queen, I was reminded of the super-railroaded adventures in 2e's reign (stand around while this Forgotten Realms novel unfolds around you!). And that adventure is a railroad from hell. (Many others have talked about that, see here and its linked articles for details.) I hope that's not how that's going to go down. Basically there have been two good runs of adventures in all of D&D history — 1. All the 1e adventures and 2. All the Paizo Adventure Paths. All the other editions have had very occasional gems amidst a sea of dross. This is one part of 2e I hope we don't retread, though the first adventure definitely seems like it.
Best Answer
The differences between AD&D 1st edition and AD&D 2nd edition is very small 2nd edition is merely a polished version of 1st edition so you shouldn't really have a problem using 1st edition modules in 2nd edition.
I asked a similar question here the answer by aramis offers a comprehensive detailing of the differences between the editions which might be of some assistance.
Also I took a look at the differences in the stat blocks from AD&D 1st and AD&D 2nd editions and they are basically identical, the 2nd edition stat blocks are just a little more organized.
I haven't played 2nd edition but I have used 2nd edition campaign settings and adventure modules in my AD&D 1st edition campaigns and I had absolutely no trouble using them, there wasn't anything i found incompatible. I basically did what your trying to do but in reverse and it worked out fine.