See it totally depends on what your interests are and what do you want to do in future regarding your career prospects. If you want to work in pure science especially in chemistry and want to further do a PhD, then it is a no brainer for you to take Chemistry in a private college.

However, if you want to pursue engineering, then you should definitely look out for engineering in a private college! So, at the end you have to go with your own calling.

You can also use our college predictor to see your chances in all the colleges:
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Hope I have answered your question. All the best!