I should say that won't make a huge difference between these two schools but bad schools have to worry about their kids even passing the state tests and don't have a lot of time for SAT prep.. I would say that the better school you are a little more likely to have been taught more vocab etc.. I went to a public school and mostly prepared outside and did fine though.. if you are smart and you work hard you can still get into a top school and make high Sat.. even if you didn't come from a top high school
NIKE, I knew a lot of people who went to Bellaire and they said SAT prep was started as freshmen. There were later SAT prep classes that were worked into curriculum. I know not so bright people (or at least avergae students) who would get 14-1500 on the old version. Given that they SAT is a test with which learning "tricks" can greatly help, high schools defnitely can make a difference in scores. Oh, just as a comparison, my high school didn't offer any kind of SAT prep or counseling. Actually, I can't really remember ever hearing much about it in school, other than "you need to take it if you want to go to college. Here is the date you can take it."