I think the difference is more about how robust recruiting is at different schools. You will have a better chance of getting an interview at the major firms. Big 4 recruiting is a good example. Many think of the Big 4 as accounting firms. They have morphed into well rounded professional services including consulting, advisory, etc. They live on campus and recruit for all lines at certain schools, recruit specifically for audit at others, and don’t recruit at all from the rest. Same thing exists in Banking and I’m sure many industries. Does GE recruit for it’s renowned FDLP (Financial Development Leadership Program) everywhere? No. They have a vetted list of schools that they visit for that specific program (based on track record and quality of students).
None of this is bad. You can do quite well working your way into great situations, but students from certain schools have an advantage in their initial job search. How they do in that job leads to the next step, whether it be promotions, MBA, etc.