What should I choose, top IIITs or NITs like NIT Delhi, Agartala, Goa, and Puducherry?

One of my friends has been researching this topic for quite some time. So sharing his views might help answer your question. According to him, it totally depends on what you are getting initially. 

• If you manage to get top IIITs like IIIT Hyderabad, IIIT Allahabad, IIIT Delhi, or others then only go for them. 
• Some courses are far better in NIT than IIIT according to the placements and other facilities that are being offered. 
• The NIRF ranking matters to a large extent. It can sometimes favor you during placements.
• The placement statistics should be kept in mind. Always take up a college that has the placement record of usually placing 90% or more.
• Do check that the placement is consistently good, decreasing or increasing.

Lastly, we can say that for choosing a particular college always consider the parameters mentioned above and then make your final decision. Because this will shape your career ahead.