I respectfully disagree.
Flagships vary in strength and range of opportunities they offer. Some are “public Ivies” and others are not, so yes there are differences IMO.
And when it comes to CS, Rutgers and Bama aren’t equivalent. The $30k/yr difference in cost (or $16k if OP gets merit $$ at Rutgers) is worth it, especially since it’s well within the family’s budget.