I don’t think your assertion that BU is more prestigious than Rutgers is true. Certainly not for corporate recruiting (which is what I have done for 35+ years). Your parents may THINK it’s more prestigious and you can certainly apply there-- but IMHO no great loss if it comes in above your price tag.
I know it’s a school which doesn’t get a lot of love in-state, but it is highly regarded as a national research U in the corporate community. BU has some fantastic, targeted programs… but there is nothing so special about any of the business majors IMHO.