Dear aspirant....!!

both institutes are good in their own way, if you want to have aesthetics centric design environment then choose NID, if you want to gain strong learning on the technicality of design then go to IIT Bombay. NID has over 15 different disciplines of Designing so the environment is very design focused. IIT B is primarily an engineering Institute so the environment is more engineering focused that's the only difference, but both Institutes have good faculties and talented students. I would personally prefer IIT Bombay for product design because of lesser fees and more exposure to engineering aspects of Design.

All the best!

Hope your query is solved!