What I loved about BECMI, but don't think it can really be replicated, was how it guided us to our game world in stages. I started playing when an older boy lent me (and later gave me) his copies of B/X. So when I started playing with my siblings and my friend, we started off in dungeons, as you do. At one point, my father saw the Red Box at the store and thought, "Oh, that's that game the kids are playing. Maybe they'll like this." And even though it was essentially the same rules, we were pretty happy to get a brand new set all our own.
Then when we got to 4th level, and started using the X-pert rules, we started exploring the wilderness. We could never find the Mentzer Expert Set until long after we didn't really need it anymore. First we started with the hex map included in the Expert Rules book, and then we started building beyond that. Our map started add new realms and kingdoms, and areas to adventure in. As our characters started reaching Name Level, I got the Companion Rules. And one of the big features of the Companion Rules was the Domain Rules. So it was like, okay, now our characters get to be the movers and shakers in the world, and we started fleshing out the political situation of our world: who was at war, who were allies, who were the Good, the Neutral, and the Chaotic realms, what the elves, dwarves, and halflings were doing, who governed magic, and so on. We made new characters who were the sons/daughters/apprentices of the original party, and who were now doing the dungeons and wilderness exploring in the world that our original party had carved out for them.
Then I got the Master Set, and I could see that now our adventures would revolve around world-shaking events and/or multi-dimensional adventuring...and that was pretty much when high school started, and we got together to play less and less, and the great Master Level adventure never got out of its embryonic stage as our days of playing D&D slowly came to an end...without any of us actually realizing it at the time. I never got the Immortal Set.
I won't say that the same kind of progression can't or won't happen with the Core Three set-up. I can only say I don't think it would have happened for us, necessarily. At least, not at ages 11-15. It was like the rules unleashed our creativity, but the staged nature of the different rule sets focused it.