The Rules Cyclopedia rocks, but I have a major bone to pick with it (and BECMI, which is practically the same thing as far as I'm concerned). Thieves freaking suck!* Their chances of succeeding at their class skills were SUPER nerfed from B/X in order to spread out their advancement over a ridiculous 36 levels; it would have been better to keep the percentages the same, then introduce some new abilities after level 14, if you ask me. Also, they could use ANY weapon in B/X, but they have new weapon limitations in BECMI. It's bad enough the poor guys have d4 hit dice, and you have to make them even crappier on top of that just to fit the new level scheme? Lame. That class deserves better if you're going to bother including it at all.
The Rules Cyclopedia is also just...a lot. It's a lot to take in. I think my ideal version of D&D would use the two B/X books as a base, and then just sprinkle some occasional RC stuff on top - some more monsters/magic items/spells here, a little rule clarification or two there, voila. Then MAYBE bring in some of the optional systems later if desired (mass combat?), but generally try to point the players to the B/X books if they need to reference something themselves, and just keep the RC to myself as an extra DM guide of sorts.
If I did that, I would probably still limit level advancement to 14, as per the Expert book. But if my players ever actually made it that far and didn't like the level limit, maybe they could budge me on that? I don't know. There are one or two Companion adventure modules that look kind of good. I don't know how smoothly you could transition from, say, the saving throw and spells-per-day tables of B/X to the RC if you switch from one to the other mid-stream like that.
Let's take a moment to compare the classes in B/X and the RC up to level 14. (Please feel free to point out any mistakes in the comments.) Experience tables are exactly the same. HP is the same.** Elf spells are the same, M-U is the same until level 12, Cleric spells are only the same until level 6. Saving throws are way off - Fighters, Clerics, and Magic-Users have worse saves by level 14 in the RC, while Thieves have mildly better saves and demi-humans have MUCH better saves in the RC. Dwarves and Halflings no longer share the same saving throw table in RC. Thief skills are generally MUCH worse in RC. The Cleric's Turn Undead table is the same until level 11 (where it maxes out in B/X), but the RC table has a lot more monsters and 2 new results, so it's hard to say if it's better or not. I don't feel like going over the Attack Table with a fine-tooth comb, but I did spot a difference or two.
In summary, switching from B/X to RC mid-campaign at level 15 would present some compatibility problems. Not insurmountable ones, by any means, but ones I'd personally prefer to address, partly to avoid confusion or inconsistency and partly because this kind of nitpicky stuff just bugs me. I would love to have something like the Holmes Basic + OD&D Reference Sheet by Zenopus, except for B/X and the Rules Cyclopedia instead. Something to work as a bridge between levels 1 to 14 for B/X and levels 15+ for the RC. Maybe I'll just have to do it myself...
*Well, I hear they're pretty good again if you use the optional Weapon Specialization rules and some other optional stuff, but I haven't really looked at them yet.
**Sort of. The Elf gets 2 HP at level 10 in B/X. In the RC, the elf gets 1 HP in at level 10 according to their class write-up near the beginning of the book, but I think it says later in the book that they get 2 HP as per B/X. I'm assuming there was a typo or an editing mistake or something. I'll probably double-check this later. It's a tiny difference either way, but I'd rather be nice and default to B/X here.