NIFT

Both institutes are entirely different from each other. NID is a premium design institute, offering B.Des and M.Des degree courses and NIFT is a premium fashion design and management institute, offering Diploma and Degree in B. Des, B.FTech M.Des M.FTech and MFM degree courses. Their courses are different from each other, except few like Textile design. NID courses are focused on particulars but NIFT courses cover broader study of any field. NID courses will lead you to a specific job, but NIFT can help you to choose multiple job options. NID has limited seats of 15 in most of their courses in 3 centers, but
NIFT is having minimum 30 seats in all of their courses in 15 centers (presently 15). Now last but the major difference is the fees, NIFT avg. Fees is 80-90 thousand Rupees per semester (for Indian resident), and
NID avg. Fees is double to NIFT per semester, varying center to center. So, "which institute is better" depends on what course you want to go for. If its fashion design then go for NIFT. If its product design go to NID. And if you are still not clear just go to their websites and see the courses and syllabus and you can also either call the institute for details or just visit it if possible. Visiting institutes before taking admission always helps to get a better idea of it.