The answer to that question is easy and complex at the same time:

All students benefit from attending effective schools. However, the least advantaged students experience the largest improvements in high-school graduation, college-going, and school-based arrests. These patterns are driven by the least advantaged students benefiting the most from school impacts on the non-test-score dimensions of school quality. However…it is the most advantaged students that are most likely to attend highly effective schools.

This quote is taken from the abstract of a new working paper by Jackson et al published by NBER. In the paper they elaborate:

Reinforcing the importance of schools, all students benefit from attending effective schools. Interestingly, even those least likely to attend college experience sizable increases in college going from attending more effective schools. This is due to the least advantaged student receiving particularly large benefit from attending schools that improve socio-emotional development. Our analysis of school-based arrests also suggest large benefits to attending more effective schools particularly for those at the bottom of the educational advantage distribution. For arrests, school impacts on both socio-emotional development and behaviours are important for the least advantaged students. Overall we show that effective schools matter, and that they may matter even more for more fragile student populations. Our results reinforce the importance of soft skills, and suggest that if one were to use test-based measures of school quality alone, one would dramatically understate the benefits for students who need access the better schools the most.

This study reminds me of a quote by Siegfried Engelmann:

Time is the big enemy of anything we do while we’re working, particularly with kids who are behind, that every time that clock ticks, we have to teach them more than a clock tick would teach a middle-class kid, or an average performing kid. (source)