Ok, to answer your question - for SAT scores in Big Ten, Rutgers would rank 8th and SHU would rank 11th. Also, from last entering class data, SHU had higher % of entering students in their HS top 10% than RU. Not saying that this makes SHU better school; rather that the difference between the two schools is much closer than some RU faithful want to accept. Even as we recruit at my firm, candidates from RU, SHU, Lehigh, Fordham, some SUNY-schools are generally considered in the same range (educationally).
My son is now a HS senior and my wife (an RU engineering alum) is dead-set against him applying to Rutgers. Not that she needed to worry, his grades and test scores are high enough to have more favorable options than either SHU or Rutgers, LOL. He and most of his friends have zero interest in Rutgers or SHU, and majority of schools in NJ. Most of these kids won't even look at them as safety schools. Maybe the New Brunswick (or South Orange) life fits for some but many kids today with higher grades want to go to schools with real campuses - UVA, Michigan, ND, Cornell, V-Bilt, Wake Forest etc. It's a hard sell to go from visiting one of these schools to then walking around New Brunswick. Even my daughter, a ninth grader, has let it be known that there is no way she would go to school in New Brunswick (tbh, I expect she'd have the same answer for South Orange, too). At least South Orange is a place one could see themselves living and raising a family. Not sure one can same the same about New Brunswick with a straight face.