While Stony Brook is an AAU, it is half the size of Buffalo in terms of research. It's a failed effort for me to even go into the workings of SUNY and the standings of the schools, because it's obvious very many people here will not buy it (probably because of negative feelings toward the city of Buffalo). The fact is, Buffalo has the most highly ranked programs, most research, and even the downstate rep of Binghamton compared to Buffalo as a liberal arts school is highly questionable, given the rankings of actual Humanities and Science departments.
I'm not even getting into the sports thing, since these schools do not try to distinguish themselves there.
Soon, Buffalo will be the only AAU of the SUNY's, one of 4 AAU schools in the entire state.
The fact that Buffalo is in a far corner of the state away from New York City hasn't stopped it from growing the fastest, doing the most research, and essentially becoming the state's flagship.