The answer to the question may be crisp and short but a government college is better than a private college any day in India for higher education.
It is a comparison between two brands, BITS and NIT. The bigger and better brand is NIT when compared to BITS.
Apart from the great brand value of government colleges, studying and being graduated from a government-affiliated college has various advantages over other top private colleges. However, the option you prefer and want to pursue is completely your choice. Consider the parameters and opt for the best.