not about the school.
If the student is equally good, Brown can send the student wherever UCB can send, and probably even more options (beyond STEM). Brown sends far higher percentage of graduates to top medical, law and business schools than UCB (for example, medical school admission rate at Brown is ~85%, at UCB is 50-55%; national average is ~40%).
The best UCB students (at pretty much HYPSM level) are likely better than the best Brown students.
However, the average UCB student is lower than average Brown student.
There is like 150-200 points difference for average SAT. That does not mean everything but it does mean something