Uhmmm...ok...Let's see what I can throw together off the top of my head (several of these are probably already in other posts, I would imagine)
Well, you mentioned the first big/noticeable one: Race as Class.
From there we go to Race AND Class...
Races in B/X-BECMI: Human, Elf, Dwarf, Halfling. Done.
Races in AD&D: Human, Elf (assumed High), Dwarf (Hill or Mountain), Halfling (Hairfoot, Stout or Tallfellow), Half-elf, Half-orc, Gnome. AND, with 1e's Unearthed Arcana, almost all non-humans get 1-5 subraces that became playable options.
Classes in Basic: Fighter, Magic-User, Cleric, Thief (available to Humans only!), Elf (Ftr/MU, basically) as class, Dwarf (Ftr) as class, Halfling (Ftr/Thf, basically) as class.
Classes in AD&D: Fighter, Magic-User, Cleric, Thief, Paladin, Ranger, Druid, Illusionist, Assassin, Monk...arguably, in appendices, Bard and Psionicist. Cavalier, Barbarian, and Acrobat added in 1e's Unearthed Arcana.
ALIGNMENT! In Basic: Lawful, Neutral, Chaotic.
In AD&D an Ethos axis (Lawful, Neutral, Chaotic) and a Mores axis (Good, Neutral, Evil) and, thus, the Nine combinations of Alignment.
Multiclassing in Basic: nonexistent.
Multiclassing in AD&D: available to non-human options in completely independent combinations, e.g. Dwarves couldn't be the same classes or class combo's as Half-orcs who couldn't be the same classes/combos as Elves, etc... Humans were allowed "Dual classing" but not multiclassing.
Equipment: AD&D had exponentially more options for armors and weapons than B/X/ECMI.
In AD&D Casting times for spells and Weapon Speeds were a thing for combat, not that we necessarily used them religiously (or at all, from game to game). Not so in Basic.
I feel like there were other "in combat" round by round kind of differences, but not really remembering what they were. Initiative was basically the same, I think...There was "Side vs. Side" combat tracking versus individual, but that was Basic and AD&D. Changed to the individual initiative we know today in later editions.
Spell lists in AD&D were significantly more beefed up than in Basic. Especially after 1eUA.
Treasure and Magic Item lists were significantly more beefed up in AD&D than Basic. AD&D had Artifacts/Relics. You really didn't get to/see "Artifact" level items in Basic until/unless you got to the "Companion" (i.e. "C") set of BECMI. B/X didn't have them at all.
AD&D had a chart for EVVVVerything. There was a %die for just about anything you needed. Basic used percentile dice much less, though both used them for Thieves Skills.
Think that's about it that i can come up with without pulling out books... So, yeah, there were some significant differences but the general playing of the game - ability scores, saving throws, how to roll attacks and damage (even if the damage die was different), and so on - was mostly the same/easily transferable.