Sumit,

The first thing you need to understand is that every NIT/IIT is institution totally funded by government of INDIA or government of State. 

Whereas IIIT are set up under the public -private partnership with agreement between government of India, government of state and private companies that's why most of the IIITs except IIIT Allahabad is  bit expensive. And being a semi private college it doesn't provide fee remission for general obc category student who parental annual income is below 5 lacs. But SC/ST students are exempted from paying tution fees only. 

NIT/IIT is fully funded by government so it provides fee remission. 

Hope you understand.