Which is better for pursuing a B.Des - the IIT in Bombay or NIFT?

For Fashion Design or Apparel Design, NIFT is the best institute in the country. If you aspire to become a designer or stylist, then choose NIFT. It offers many design specializations such as Fashion, Accessories, Textile, Leather, Knitwear, etc. 

For Visual Communication and Product Design, IIT Bombay will be better. IITB basically offers Graphic Design, but it has more importance due to the IIT tag.