Copying over my response from a similar thread on Dragonsfoot:
Comparing RAW 1e to RAW B/X, the most obvious thing is that there's a lot more stuff in 1e. More characters, more races, more weapons, more armor, more equipment, more spells, more monsters, more magic items. Many, many players have both intentionally and unintentionally used 1e as a supplement to B/X, by adding these various 1e elements to their game without changing the actual mechanics of running their game.
When you look at the procedural rules, several items stand out:
1. 1e had way more modifiers to pretty much every procedure. Surprise, initiative, monster reactions, to hits and armor class, morale... all of these rolls are far less static from instance to instance in 1e than in B/X, with different modifiers coming into play with each new situation. In B/X, the modifiers are more likely to stay the same from roll to roll.
2. Related to #1, the monster reaction, morale and loyalty rules are much simpler and more integrated together in B/X than in 1e. I've found that in practice, this makes these rules far more used in B/X than in 1e which in turn makes Charisma a more valued stat in B/X.
3. Spell casting is much more complicated in 1e. The spells themselves are more complex, with more exacting descriptions and more variable effects. Added to this are spell components, casting times, and more complicated spell access and research rules. It's harder to be a magic-user in 1e than in B/X, but the 1e magic-user tends to be more versatile, with more spells to choose from that can perform a larger variety of functions.
4. 1e is more forgiving at low levels, with a negative hit point rule, clerical healing available from first level, and low-level characters with more hit points. The only thing that counter-balances those items in B/X is the cheap plate mail armor.
5. The 1e rule that you cannot strike in melee until the round after you engage unless you charge gives combat a bit of a different dynamic in 1e.
6. 1e has a few sub-systems that are completely alien to B/X - unarmed combat and psionics being the big examples.
7. There are no explicit rules in B/X that require cost and time be put in to training. AD&D characters tend to be poorer and more money hungry. They do, however, have the advantage of magic items being a significant portion of their earned experience.