Hello Aspirant,
See NITs are those engineering institutions which comes under the direct control of Indian Government but the IIITs run on Public-Private partnership die to which some irregularities may occur in IIITs. Being the central institution NITs get special privileges from India Government and hence they have name and fame, not only due to special privileges but also through their quality education, practical skills and so on.
You should go with NIT if you are getting option between the two.
I hope this information helps you.
Good Luck!!
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