You can bet that public school kids will be much better at team athletics. It's pretty hard for one Mom to churn out a basketball team, much less a football team where all are eligible for the same level of play at the same time. Basketball, I think, would require 3 sets of twins in 3 years. Triplets or quads would help. (Three pointer with a foul = 4.....lol.)
Homeschoolers are smokin' on the spelling and geography sections. I'll bet also that they're better in basic subjects for those parents who actually home school as opposed to those using "homeschooling" as a dodge.
I'll also guess that "institutional" high schools (large facilities whether public, religious, or private) will churn out better prospects in higher math, higher science, and higher arts. Why do I say this?
I don't think most home school parents have the background in calculus, advanced science and art, nor do they have the facilities (labs) to make these things readily available to home schooled kids. Maybe computers will change that, but every "long distance" or "computer" class I've seen doesn't compare to a knowledgeable teacher who is PRESENT for questions and guidance.
As for higher science and math, it's important to point out that parents who aren't proficient can supplement such subjects with tutors or co-ops, entrance into the ps high schools, or community college classes.
You just haven't been creative enough or done enough research if you think homeschoolers are limited by being home even in athletics or higher math and science. This just isn't the case and the beauty of homeschooling is once high school years hit and a child shows an obvious talent or proficiency for something, they can devote more time and attention to it, actually making them the superior candidates in the long run. Just a few random thoughts;-)
My family is fortunate because my husband is brilliant in math and science. He teaches my son in the evenings. He and my son enjoy this interaction. My son scored a near perfect on his SAT's regarding those subjects. (My son just turned 14.) We know homeschooling parents that aren't as proficient in math and/or science, but their kids do just fine by utilizing used textbooks, the internet, software programs, science museum seminars or hiring a tutor. (My husband tutors one of my son's friends in math.)
My husband was never that keen on biology so he has our son attend a Santa Rosa Junior College course. My son will probably take a chemistry course next year even though he and his Dad have set up a pretty good lab in the garage.
Of course, not all homeschooling families can afford tutors, expensive software or internet courses, but somehow they manage. If their child is motivated and talented in certain subjects, all sorts of options (and blessings in regards to funding) open up! I've seen this happen time and time again.
Most homeschooled kids have parents just like me. I know where I am weak and I get extra help for those subjects. For science, I have found an retired NASA scientist who loves teaching homeschooled kids. For upper level math, I am using a video program and my son is regularly scoring between 89 and 95 on his algebra tests. I can't teach violin, so I get a private teacher, who's own daughter is now studying at Julliard. For art, I have found an artist who teaches out of her home who on the side sells her artwork for upwards of $25,000 per piece.
As a homeschooler, I have many more options for my children. I can zero in on my children's interests without any interference. I don't have to wait for some school official to take note of my child. I don't have to work with ANY middlemen.