Yes, one of my friends strongly regrets giving up on BITS Pilani just because of the high fees and went for a low-ranked NIT instead and to date regrets his hasty decision. He wanted to pursue MSc in Economics from BITS Goa but he had to take civil in NIT.
He stated that the condition of core placements in NITs was pathetic and the average package was as low as 3-4 LPA. Only non-core companies visited for placements while his friends that chose BITS Goa MSc in Economics got excellent internship offers from JP Morgan Chase, Credit Suisse, etc. Moreover, the BITS Pilani dual degree places students in good IT, Analytics firms as well.
My friend's career has been set back by 3-4 years in comparison to his counterparts and it will take years to reach the salary package they are currently receiving. He now considers his last options as GATE, PSU, or MBA.