I chose EPGY for my kids, who are still in early elementary school, because until recently AOPS only offered courses for algebra and more advanced math subjects. AOPS is now offering pre-algebra. EPGY is probably easier than AOPS when comparing courses on the same subject. Most EPGY problems are fairly straightforward computations -- for example factor (x^2 + 7x + 12) in algebra. For children in elementary school I think it is reasonable to use EPGY through the beginning algebra course, because it is not that expensive through Open Enrollment (OE). Once EPGY OE offerings are exhausted, their courses become much more expensive, and AOPS may be preferable for keen math students. This is probably what I will do.
In general, EPGY math seems to target students who will use math (engineers, physicists) while AOPS is targeting students who may want to be mathematicians.
Alcumus is a free AOPS resource. It could be supplemented with AOPS books without signing up for an AOPS course.
