So ... there are a few different factors here.
First, I have to reject your premise. Sorry, buddy, but- "B/X lasted only two years" isn't (IMO) correct. Let's start with the basic history as I know it-
OD&D (from brown box through supplements) was 1974 - 1976.
AD&D was from 1977 (PHB) but wasn't playable as AD&D until 1979.
B/X or BECMI was from 1977 until ...
Still not quite right.
The timeline goes:
1974: Original D&D is released
1977: Basic D&D (edited by Eric J Holmes) is released. This is an introduction to how to play Original D&D, including a couple of concepts from the Greyhawk supplement, and a very few from the in-progress AD&D books.
Now, the Holmes version of Basic D&D is very much a cut-down version of OD&D, with a few house rules (for initiative) thrown in. You can see this most clearly from the ability score adjustments - Strength, Intelligence and Wisdom *only* affect XP gained (giving a bonus) and have no other effects. Constitution uses the Greyhawk progress (15-16: +1 hp/die, 17: +2 hp/die, 18: +3). And Dexterity gives only a +1 or -1 to missile attacks.
Although it sort of treats races as classes (with all halflings and dwarves being fighters, and elves being fighter/magic-users), the elf splits XP between two classes. Incidentally, you have to roll to hit with magic missile! (2-7 damage if it hits!)
1981: Basic D&D (edited by Tom Moldvay) is released, along with the first Expert Set (edited by David Cook). This is the edition referred to as B/X.
This edition is a major rewrite of the rules to make them clearer. (Holmes is, like OD&D, often arcane). The rules are written brilliantly, and it introduces the ability bonus progression of 13-15: +1 ,16-17: +2, 18: +3 that would become so familiar to people playing Basic D&D.
This is still based on the OD&D system, but some elements would be unfamiliar to people who had been playing the older system. Each monster is explicitly given a 2-12 Morale score. Elves, Dwarves and Halflings are explictly classes, with each (and especially the elf) having its own progression table. Magic Missile automatically hits! Mostly, it feels like a far better organised system.
1983: Basic D&D (edited by Frank Mentzer) - the Red Box is released. This is the famous one. This is the one that would be the primary boxed set for the next eight years (until it's replaced in 1981 with the Black Box), and sold huge numbers of copies.
This edition splits the rules into a Player & GM book. The Player book is primarily notable for the Choose Your Own Adventure style of introducing the player to the game. However, the underlying rules are unchanged from Moldvay. The Expert set would make some changes to character progression, so as to make room for the later Companion and Master sets. However, otherwise the rules are very much just a reformatting of the Moldvay/Cook rules.
Unfortunately, the reformatting made the books rather inelegant. Same rules, right? So, it takes Moldvay 64 pages to explain what takes Mentzer 112 (64 Player book, 48 DM book). The Companion rules were pretty interesting, as they added Kingdom Building to the mix, which was awesome. The Master rules were... less good.
This edition, in full, is known as the BECMI rules. It would be reformatted later (in 1991) with the Black Box, the Rules Cyclopedia and Wrath of the Immortals. And then that stuck around until the Basic line was shot and killed in the late 1990s.
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The B/X rules (Moldvay/Cook) were around for two years, then survived as the foundation of the BECMI line. But, due to their elegance, people still admire them over what came later. Holmes might have written a version of Basic D&D, but the 1981 set was a revolution in how the rules were written.
Cheers!
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