Hello, 

As per your requirement, i would say that nit tag is important but not to that extent that it is what matters. Aftrr btech, what matters is your cgpa of btech course and your placement chances and your gd pi etc rounds. 

As per your querry, if you get in bit you should go for it but fees would be higher but its highly reputed collegr.

But if you only want to get chance in government college- and have nit tag than drop a yr but dropping 2 yrs is not a much issue as you are ekigible for jee 2020. 

Do what suits your better. Both have advantages and disadvantage so do what better for you.

Good luck