I'm with you. in some cases, the disparity is even greater than it is between the hypothetical schools you listed. Jonathan Kozol's text, Savage Inequalities, shows an example of this by looking at two schools in the same county in New Jersey. I forget the specifics, but one receives something like $10,000 annually per student in funding while the other sees just a few hundred dollars.
in schools like the latter, textbooks are not only antiquated, but also limited; they are often shared between multiple students, leaving many with none to take notes or study from overnight. classes are taught in supply closets because the schools have inadequate space. the teachers are often less experienced and skilled than the ones in the wealthier district because those ones get the higher-paying jobs.
the result is that not very much is learned, standardized test scores (flawed measure of knowledge though they are) suffer, and drop-out rates are high. obviously, these are social issues as well as academic ones, but the point is that education can't be entirely divorced from resource availability or school quality.
I'm as charmed by the notion of the autodidact as anyone, but it's hard for me to assume the poor performance of the less fortunate kids is their own doing rather than an uneven playing field. and let's not forget that, to teach oneself, one must value learning and be motivated to pursue it. how valuable does education seem if one's school / town / state can't even supply him or her a textbook or a classroom?