@honeyharasho - Well, I’ll try to address your questions. EMF looks like a very intriguing program, but unfortunately I don’t have direct experience with it, only what I can glean from looking at the curriculum and some of the source material and problems. It looks to be “deeper” than most math programs, with a nice introduction to rigorous math at a very early age that I would think make sense for talented kids. There is a huge difference between college level math (past the basics like calculus) and the more algorithmic approach of high school math. AoPS and the competitions seek to bridge this gap by having kids struggle with problems, which encourages a flexible approach, while EMF seems to favor a more axiomatic, proof-based approach starting at a simple level. I think if I had to chose one, I’d go AoPS, both because it will be more practical for the many competitions out there (and just as in athletics, the “good” math kids find each other in the competitions, not in their regular classes, just like athletes don’t bother much with PE class), and also for the strength of the community through the forums.
It’s worthwhile I think to see if you could substitute AoPS for regular classes, but I know schools won’t give you a discount for skipping their math classes! I’ve said it a number of times on here, but no regular school (except maybe the Proof School in San Francisco) is going to approach the rigor of AoPS, and no group of kids is going to be as capable. There is a reason that just about every talented math kid is on AoPS.
About missing out by studying the books and not attending course, I do think you miss out a good deal, especially with regard to the feedback you get in the class on proof writing. A disciplined student could of course get the lion’s share of the experience from just the books (which are great), but for that last bit nothing beats being part of the class. But that only really applies to the standard curriculum. I don’t think that the competition focused courses are that worthwhile, until you get to the AIME level (WOOT is also a great course for kids targeting USAMO, but that is going to be a few years down the line for your son). For competition, nothing beats doing lots of problems and participating on the forums. There are some terrific kids on there.
I hope that helps!