Which is a better option to pursue BBA among a university and an institute?

It hardly matters whether you do your BBA in institute or in university. Quality of education and good faculties, infrastructure, exposure to business etc. matters. So, you can choose any one of the two options and take admission.

You may refer to following link for list of top BBA Institutes in India: https://www.shiksha.com/bba/ranking/top-bba-colleges-in-india/93-2-0-0-0