I believe size definitely matters in US due to size of country. Bigger schools are in big population centers so there are more numbers and the probability of having better soccer players goes way up. Population centers have more middle/upper middle class and therefore more kids who play in soccer clubs around these population areas due to costs associated with club soccer and availability of good soccer clubs in these areas.
Making the club comparison, just look at the top clubs around - CSA, CASL, Concorde, etc. These are all around large population centers. Just ask the DoC's of SC clubs if these larger clubs have advantages due to size. Compare the percentage of kids playing club soccer in Westminister to Columbia, Charleston, Greenville, or even Rock Hill.
This is not to say that a smaller school can not have some good years with an "unusual" number of talented soccer players and I will even say that in some years they could compete with their larger school brethren. Also, some (and I mean a few) better smaller school programs can beat larger schools that have little soccer tradition, but I do not think you can use these few examples to make an overall generalization.
If you took the top 5 (preseason) schools from each classification and they all played each other, I do not think the 1A or 2A schools would pull off too many favorable results maybe with the exception of some of the private schools.
The private school results are a bit misleading also. Private schools tend to be around big population centers (Pinewood Prep, Bishop England, Cardinal Newman, Christ Church, etc) and if you can afford to send your child to private school, having your child play club soccer is probably not that big of an additional burden and since you are in a big population center, you have the resource available. The private schools can also afford to pay for some talented coaches not only through salary, but can also offer their children scholarships to attend highly respectable academic institutions. So, while these schools are small, they have a concentration of talent and an advantage of coaching that is not typical of similar size public schools that will tend to be in rural areas. If you look at the preseason rankings (and even past year results), Bishop England is atop 2A and Christ Church and Southside Christian are atop 1A. I am not even sure it is fair that these schools are allowed to play in the smaller public school classifications. They should all just have to play in SCISA.
Sorry for the long winded post
