So, I was going to get back to this, but I've been busy. There's a fair amount to unpack here!
Let's start with nomenclature.
Holmes- the 1977 Holmes "Basic Set."
B/X- the 1981 Moldvay revision of Holmes (the new "Basic Set"), including the Expert Set by Cook.
BECMI- the 1983 "Red Box" by Mentzer that so many are familiar with, along with the later Expert, Companion, Master, and Immortal Rules.
RC- the 1991 revision and codification of the Basic, Expert, Companion, and Master rules.
There are two things that are worth noting- first, these are all different. Second, the biggest difference is between
Holmes and everything else.
So let me explain. Holmes was tasked with creating a Basic Set (hence the term!) that would simplify the core rules of
OD&D and allow players to transition to the forthcoming
AD&D.
So
Holmes has many of the hallmarks of what we would later consider
de rigueur for a Basic set- it only dealt with levels 1-3, and explained the game and introduced key concepts. But while it introduced ideas that would later be used by Moldvay when he made his basic set, it was fundamentally a different product- it's really an attempt at simplifying the OD&D rules, and it has a muddled conception of race (using race as class, but also explaining that the ability to differentiate race from class will be present in AD&D).
B/X, on the other hand, is an entirely new ruleset. There are certainly background issues regarding this (Arneson/Gygax litigation), but this is the real point of differentiation between AD&D (1e) and a completely different ruleset (that uses, for example, race-as-class). Many people, including myself, thing that the Moldvay/Cook Basic/Expert set remains one of the best, most elegant rulesets designed for D&D. So while a person can say that
B/X continues some of the concepts in
Holmes (such as the emphasis on clear instruction, and breaking out levels 1-3), it is the beginning of a completely different branch of D&D.
BECMI has some changes from
B/X. While people can, and do, quibble about some of the minor rules variations, the most significant changes are in the layout, instruction, and effect of having future editions (the CMI).
The one area where Mentzer is slightly superior, in my opinion, is the layout/graphics presentation. It really shines here. However, the tone/instruction/clarity of the rules is much better in the Moldvay rules. In addition, by having a natural cap of level 14, the progression of character levels makes a lot more sense.
The
RC is a codification/resources for people who played
BECMI. It doesn't have the "I" (Immortal) rules because, um, they are crazy. It contains some extraneous stuff (such as some skill stuff) and presents various material from the Master/Companion series retroactive to the beginning (think classes, like Druid and Mystic, that might clutter up the presentation of
B/X).
This is the short and sweet of it all.